I've posted on this at least twice. Please try and actually read what I write. For the third time, my answer is no. I assume that your reasoning is that if the sample space is infinitely countable then the probability of each element of the space must be 1/infty=0. But, in fact, that would violate the axioms of probability, because the sum of the probabilities of each element would be 0, and not 1, as the axioms require. When the sample space is uncountably infinite, the probbilities must be unqual, so that they can sum to 1. A couple weeks ago, I gave an example of a valid set of such probabilities in which (furthermore) none of the individual probabiliies were 0.