If the number generator is truly random, the probability of it choosing a particular number for Adam is 1/10 and for Bethany 1/100, but this is different than stating:
"The probability of Adam guessing the correct outcome is 1/10, whereas it’s 1/100 for Bethany".
Why? Because there might be any number of factors which make it more likely that Adam and Bethany will choose a particular number over others. For example, perhaps Adam heard a particular number repeated on the radio earlier that day, or perhaps Bethany's favourite number is 27. This in turn impacts the odds that they will choose other numbers, although we are often unaware of such biases when arriving at probabilities.
It is important though to realise that we use probabilities most often to make predictions about the future, and that we shouldn't confuse the conclusions we draw about those probabilities with the notion that these probabilities actually exist.
When an event happens, we have no way of knowing for certain that it could ever have happened otherwise. All we have to go on is a sample size of 1. You might postulate the odds of a 47 year-old, chain-smoking, alcoholic habitual drunk driver dying on any given day to be about 1/18,647,236, but if that person actually dies, there's nothing we know about probabilities that suggests they could have died at any other time. (Some might argue the unpredictability of quantum processes might be an exception to this idea. I don't know enough about quantum mechanics to make a confident statement either way. Someone else might clarify).
As for:
"Something about this seems to create the implication that it’s “harder” for nature to create the first event instead of the second".
A number being chosen at random (if a random number machine is truly possible), upon being 'asked' to do so is inevitable (barring malfunction/interference). The 1/100 generator may have to do more 'work' at some level in order to select a number (if, for example, it works via a digital 'shuffling' of the numbers prior to selection), but I don't think this is what you're referring to. The 'event' would still, as far as we can determine, have been inevitable; perhaps a part of a causal chain of prior events. From this perspective, comparing the probabilities of events that have occurred might be deemed either easy (if you assert that all events have a probability of 1), or impossible (if we admit we can't know if randomness truly played a part).