The answer to that question is obviously 0%
Now, what would be the answer to the same question with the answer options:
A) 20%
B) 40%
C) 60%
D) 20%
E) 0%
Now, what would be the answer to the same question with the answer options:
A) 20%
B) 40%
C) 60%
D) 20%
E) 0%
0% and 100% are indefensible for any uninformed prior.
There are two answers giving the correct probability for uniform prior. One of the 25% is a wrong answer despite being indistinguishable. Such a thing can happen because of a typo or in any myriad of ways. It's not a paradox.
If it asked the question "knowing that probability of success for random single choice question out of 4 answers is 25%, what is the probability of selecting the correct answer at random from one of the below?" That formulation implies an informed prior.
That'd have the answer of prior% with 50% for uniform prior, but it's not duplicated, so the actual answer is 0% making it a paradox. If it were duplicated, (answers only 25% and 50% available) the either answer of 50% would hold.
But that was not the question asked in yours or former question.
If none of the answers are correct, the chance of picking the correct answer is 0%.
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.
Maybe I'll go for a walk.
Given uniform random none of the answers is correct:
25%) There's a 50% chance of choosing this answer
50%) There's a 25% change of choosing this answer
60%) There's a 25% chance of choosing this answer
If you're allowed to pick your own random distribution then any answer is equally valid. Say we pick one of the 25% answers 25% of the time, and the other ones uniformly:
25%) There's a 25% chance of picking this, as defined by our random distribution.
50%) 37.5% chance
60%) 37.5% chance
But if we instead pick our distribution so we pick the 60% answer 60% of the time and the others uniformly we've suddenly got this answer:
25%) ±27% chance
50%) ±13% chance
60%) 60% chance
So depending on if you interpret random as "uniform random" or as "whichever random distribution you like" either none of the answers are right or you can pick any answer to be right.
Sorry but that seems disingenuous... You are ready to accept that there's a mistake in one of the answers but not that none of the answers are correct?