It's really quite simple.
if the correct answer to the question is 25%, then both A and D are correct, in which case the probability of randomly picking a lettered choice with 25% as the answer is 50%. This is a contradiction, so the correct answer cannot be 25% If the correct answer is 50% or 60%, then the probability becomes 25% in either case, and again a contradiction. Therefore, the correct answer to the question is 0%, which is not an available choice. And so, the probability of randomly picking a lettered choice with 0% as the answer is still 0%, and this answer choice is self-consistent.
This is an exercise meant to illustrate the difference between a question that is solvable with math and logic and one that requires "outside the box" thinking. The idea that "all answers are incorrect as written, and therefore with that answer-set, the problem is unsolvable" illustrates the "inside-the-box" thinking that the correct answer must be one from the set provided. In fact, the question "if you choose an answer [IMPLIED: listed below] to this question at random, what is the chance you will be correct?" has a definitive answer: 0%. Because if you choose ANY of the given choices at all, you have a 100% chance of being wrong.
Even if you assume that you can choose any percentage at all, between 0% and 100%, allowing all fractions of a percent, the chance of it being correct is the limit as it approaches 0.
Now.... consider what happens if the answer choices are listed as follows: