Hehe, there's a 33% chance to choose 25%, 33% for 50% and 33% for 60%. No answer fit the chance, so 0%.

But what should D) be instead, for having a valid answer?

Or, if you're arbitrarily choosing A) B) C) or D), you have a 50% chance of choosing 25%, and a 25% chance of choosing 50%. The intuitive answer is 25% in a four-choice multiple choice, which would make 50% the correct answer (since there are two 25% answers), but in that case the answer is 25% (since only one answer says 50%), but... so on and so forth.

If D) was something different there are a few interesting possibilities -- if D) is 0% you could toy with the idea that none of the answers are correct (we haven't actually established that any of the answers are correct), except that it would make D) correct, making it incorrect, so A) would have to be correct because one of the answers other than D) must be correct.

If D) was 50% then I'd say any answer other than C) is correct, kind of. There's only one 25%, and if it's deemed "correct", then there's a 25% chance of picking it. But with two 50%s, there's a 50% chance of picking that, so it could be "correct". Is its correctness determined by you picking it and then deciding if it holds true for it to be correct? Then you have a 75% chance of picking a correct answer and none of them are correct. Unless C) was 75%. Then I think we get another paradox.

Then again, I'm not very good at probabilities, and have been wrong here before

If you rewrite the question
to
The only answer you would get is B.

The only other argument you could have is it's never ending self-reference, therefore never being able to give an answer.

The question does not ask whether A,B,C or D is correct, but the probability that you pick the correct out of 4 answers. So the intuitive answer is 25% (not A or D, but 25% or 1/4 or 0.25).
However, the text is missing important information such as how many answers are correct or if they are all wrong. Additionally, the text does not state that you (can) pick A,B,C or D with the same probability (it only says "at random" but that does not mean anything) because the percentages may affect you.
Therefore it is not a mathematical question of probability and thus you can argument that all probalities 0-100% can be correct. Instead it's a question to fool you and to create a discussion and I guess it will always be successful.

I think, the chance to be right, or not, is always 50%. Because it is binary. You can be right, or not - there are no possible values between.

And 50% is one of the possible answers (B). So it is possible to finde the correct answer, which is 50%.
If the answer B (50%) would not exist, the chance to be correct will be 0%. But it exists, so the chance is 50%.