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>0% and 100% are indefensible for any uninformed prior.

If none of the answers are correct, the chance of picking the correct answer is 0%.

Again, not for a question that has a defensible answer present when you're picking at random. (Uninformed prior.)

If there is no defensible answer present, it's still not 0%, it's a paradox.

The answer is dependent on base axioms accepted. (Axiom of choice and axiom of regularity are a few.) The answer set is Dedekind-finite and countable, whereupon probability is 1/logically consistent answers given the axioms chosen.

Wake up, check HN, see a lively argument about whether something that can't happen has a 0% probability of happening or not.

Maybe I'll go for a walk.

Of course, a uniform distribution is implied. The fact that you choose to misunderstand this on purpose, doesn't make you smart or right. It makes you a pedant who is still wrong.

Not quite. Because the chance is 0%, the fact that you were able to pick the choice (with 0%) at all implies a contradiction.

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