First a bit of terminology: We can divide processes into two categories: accidental processes which happen mechanically, naturally with no purpose guiding them, and teleological processes which have a purpose guiding them. A teleological argument is an argument from the existence of apparent purpose in an object. It's basic framework is this:
A. There is an object x. The structure of x is functional; it is suitable to serve a purpose.
B. There is no accidental process which could have caused the observed functional structure of x.
C. There is a teleological process which could have caused the observed functional structure of x.
D. Therefore, the structure of x came about by a teleological process.
ID, or Intelligent Design is a collection of teleological arguments and supporting arguments about the origin of the universe and of life. The universe argument argues for a teleological process in creating the universe; the life argument argues for a teleological process in creating life. Neither argument is specifically an argument for the Judeo-Christian God, but they can be used as supporting arguments.
The question misconstrues the two primary ID arguments in the following ways:
The arguments are not probability arguments. Probability only comes afterward, to counter counter arguments.
Neither argument relies on a prior probability or assumption of God's existence.
God's motives or purposes are no part of either argument. That is, there are no premises of the arguments that say God wanted the universe to exist or that he finds life valuable.
The arguments do not crucially rely on a prior knowledge that things like the designer exist.
The teleological argument schema is used in many places. Here are a few examples:
A security guard finds a door unlocked that was locked the last time he made his rounds. There is no accidental process that could unlock the door, so it must have been unlocked by a person.
A paleontologist finds that a rock contains a structure like a leg bone. No accidental process would produce that structure within the rock, therefore the leg bone structure came about through a biological (teleological) process and was later incorporated into the rock by an accidental process.
An archeologist finds a stone that is shaped like a hand axe. There is no natural process that would lead to that shape and also lead to the stone being where it was found (if the stone had been found in a river bed, the argument would be a lot less plausible). Therefore the stone was crafted by tool makers.
A SETI researcher detects a signal which contains a sequence of the first seventeen prime numbers. There is no astronomical process which would produce this signal, so the signal must have been produced by an intelligent signaler living in another solar system.
None of these arguments relies on a prior knowledge of the existence of the agent who made the artifact. In fact, they may all be used as evidence for the existence of someone or something that was not previously known to have existed: an intruder in 1, a new species in 2, tool makers earlier than any previously known in 3, and extraterrestrial life in 4. It is the same with ID. The ID arguments may be used as arguments for the existence of an agent capable of creating the universe and of life. This argument is not circular in ID any more than the SETI argument is circular.
An opponent may attack a teleological argument in one of several ways. First, he may attack premise A by arguing that the supposed functionality is not functional at all. I don't think this attack is relevant to the ID arguments.
Second, an opponent can attack premise B by proposing an accidental process that could explain the existence of x. For the ID arguments the primary counterarguments of this sort are Darwinism, the accidental universe, and the multiverse. By "accidental universe", I mean the position that we don't know what sort of universes are possible, so it may be that the only possible universe is one that happens to support life. This is where probability comes into the universe argument. The fine tuning argument (the argument that a life-supporting universe is highly improbable) is properly viewed as a counter counter argument to the argument that a single accidental universe would support life.
In the biological argument, probability comes in to oppose Darwinism. For example, ID proponents have calculated that by current biological knowledge, even a single major structural change (say, from single body segment to multiple body segments) is astronomically unlikely, even given impossibly generous assumptions about the number of chances for such a mutation. If they are right then Darwinism is not a viable theory.
Note that in neither case is probability used to support the existence of God; it is only used to counter the position that there is an accidental explanation for x.
A third way to attack a teleological argument is by denying C--denying that there is a teleological process that could have led to the existence of x. In the case of the ID arguments, this argument takes a specialized form: that there is no teleological agent that could have made the universe or made life.
I said earlier that it is common for teleological arguments to conclude the existence of previously unknown entities, but opponents of the ID arguments do have a better case here. In other teleological arguments, the previously unknown agents are agents of a type that are previously known to exist. We know that there are people with keys or lockpicking tools, we know that there are animals with legs even if not exactly that kind of leg, and we know that there are toolmakers, even if we did not know there were any at that time and place. Even in the case of extraterrestrials, we know of natural living organisms, and can reasonably extrapolate that there might be some of them elsewhere in the universe.
By contrast, God is not of any type that is otherwise known to exist except in the general sense that he is a being with a mind. But to have created the universe, God would have to have some rather extraordinary properties. To create life he would have to have some rather less extraordinary properties. Speculating that (a) there is some other sort of life other than organic, (b) that evolution for this sort of life is far more probable than biological evolution, and that (c) this life evolved and created life on earth strikes me as not much more extraordinary than the SETI speculation.
Still, in defense of the ID arguments, keep in mind that what they are discussing are rather extraordinary objects (the universe and the biosphere) and it would be expected that the origins of these objects would be extraordinary whether they were the result of accidental processes or teleological processes. Though we have no independent proof of the existence of any being that could have created life on earth (whether natural or supernatural), neither do we have any idea what sort of chemical process might have led to the first life or led to the major changes in body structure that would have been needed for life to have evolved. And neither do we have any idea what sort of accidental processes might have led to the Big Bang or any other origin of the universe--especially given that we don't even know how processes could have existed before. In the environment of such lack of knowledge, postulating the existence of an unknown designer does not seem particularly more ambitious than postulating the existence of unknown chemical processes or unknowable physical processes.