In St. Thomas’s third way, he says, “that which is possible not to be at some time is not.” Basically he is saying that if something is possible, it will be actual sooner or later. Is this really the case?
With some qualifications, it is indeed the case. If the probability of something during equal units of time remains fixed, or if it does not decrease sufficiently quickly, then at the limit of infinite time, the probability that the thing will happen sooner or later will converge to one. Thus, to give an arbitrary example, if there is a chance that human beings will produce a space elevator during the next 20 years, and the chance for each period of 20 years is not constantly decreasing, then it will happen sooner or later.
Of course the qualifications imply that there are still plenty of ways that this could fail to happen, as if time does not go on forever, or if something happens (e.g. the kind of thing that might be called “the end of the world”) that reduces this chance to zero, or that causes it to start going down, and to continue going down forever, quickly enough that the total probability converges to something less than one.
It might be possible to argue against St. Thomas’s application of this principle in the third way, since even if we believe that it could have happened that nothing existed, we might reasonably suppose that once something exists, the probability of “nothing exists” being true in the future is immediately reduced to zero. Nonetheless, it is certainly true that the existence of contingent beings implies the existence of a necessary being.