Btw, if one assumes the existence of the infinite in mathematics, an event CAN be classified as having both a probability of zero of occurring, and still be possible.
Let us, in the spirit of the attempt, use the greek letter Epsilon - usually left for the extremely small, as the variable assigned to said probability.
There would then be 6 possibilities to consider:
1) Epsilon=0, and no deities exist.
2) Epsilon=0, and at least one deity exists.
3) Epsilon is between zero and one, exclusively, and no deities exist.
4) Epsilon is between zero and one, exclusively, and at least one deity exists.
5) Epsilon=1, and no deities exist (Talk about false hope)
6) Epsilon=1, and at least one deity exists.
If the question is false, it would eliminate a small sliver of the possibilities. Really if any of the six could be eliminated, or certainly determined, I'd like to see where it would lead?
While the question might not be determinable in any sense, obviously, I'd just like to hear takes on this! Hopefully something of value has been added?
***Upon further thought, I believe that epsilon would've equaled zero in Bertrand Russell's brand of agnosticism! He used an example of a teacup floating in space, and the odds that it would be there. Had the man put more time and energy into it, the examples would've gotten even more bizarre! In mathematical terms, the probability, as he would've put more and more time into it, would've APPROACHED zero while whatever was under consideration would've TECHNICALLY remained possible! This in itself is a question of whether the characterization of Bertrand Russell's theological views can be described in this way!?