I find with ideas like this that probability doesn't really play a role. I don't think we have enough information to be able to justifiably say whether its probable or not. We are entitled to guesses using our intuition, ofcourse. I don't even have that in the case of quantum infinity - but I do think its possible.
The problem is that this line of thinking has gotten people into trouble before. The word atom, for instance, means indivisible. Protons and neutrons were regarded as some to be fundamental. Every time, though, they were
wrong. Science isn't about having convenient beliefs that make us feel good. Its about truth.
Personally, I don't care one way or the other whether there are an infinite number of elementary particles, or if there are an infinite number of quantum levels. But that could be the case, and we could be contemplating the true state of reality in that respect, something which not everyone has the luxury of doing. For those of us who have a deep interest in the nature of reality, its cool
Ideas like an infinite number of elementary particles, infinite quantum levels, eternity, etc. aren't ideas that belong to the realm of science, but they belong to the realm of philosophy. So, if scientists make serious reference to these ideas as they relate to their hypotheses or theories, either rejecting or accepting them, I think that is when it becomes clear that their ideas are beliefs.
I think its worth keeping ideas like that in mind. They certainly shouldn't be dismissed altogether in favor of a belief in a hypothesis or theory which claims that at one point or another there is a planck length. This kind of a belief is just as bad as a belief in leprechauns. Worse, actually. Polluting the world of science with such beliefs is serious business. I really don't like to see science become like a religion to some people. Its disappointing, and worrying because those beliefs might spread.
I find that some are, but some aren't. Some become closed minded without even realizing it when they accept cetain ideas as true, like say accepting that neutrons are fundamental particles, or that quarks are fundamental particles.
No doubt there are many scientists who say that. But, just as atoms and protons were discovered to not be fundamental, the same thing might happen with quarks. The fact that we don't see deeper at this time isn't an invitation to adopt all kinds of beliefs regarding the nature of matter at those quantum levels.