However, even if one is willing to assign zero probability to events that contain inherent logical contradictions, that’s not at all the same as assigning zero probability to a claim about the empirical world.
If claims about the empirical world can have arbitrarily small probability, then a suitable infinite conjunction of such claims has probability zero, just as surely as P(A&~A) does.
If claims about the empirical world can have arbitrarily small probability, then a suitable infinite conjunction of such claims has probability zero, just as surely as P(A&~A) does.