You're right, I should have said "proving non-existence".

As for the Occam razor (and any formalizations thereof) it's still 50% for an arbitrary proposition P. You need evidence (for instance in terms of the complexity of the proposition itself) in order to lower the probability of the proposition.

Otherwise I can just present you with two propositions P and Q, where Q happens to be non-P and you'll assign the same sub-50% probabilities to P and Q, even though exactly one of them is guaranteed to be true. I think that would make you exploitable.