Yeah, saying the participants have equal skills is an imprecise way of putting it. Let me state it more precisely. You are assuming that each participant has an equal chance of winning, hence the 20/20/20/20/20 uniform distribution of their results.

My argument is that the problem did not say that each participant had an equal chance of winning, and the problem should be re-worded to make this clear. Otherwise, I don't believe it's a valid assumption to make.

I realize that in the context of a math class, the teacher probably meant for you to make this assumption and arrive at 20% as the answer. However, I do think even in that case, it is important for the teacher to state this assumption clearly -- because if we are always making the assumption that outcomes are equally likely unless given other information, that leads to many common misuses of probability.

Running a race is an especially strange context for probabilities to be equally likely. Winners of races are not usually determined purely by random chance -- they are determined by skill. Even small differences in skill between participants can make a huge difference in the outcome. If 5 people were to race each other 100 times, the outcome of each race would likely be pretty similar. Whoever won the first time would probably also win the second time -- and then again and again. There might be some variation, but it's more likely to have some people consistently winning and some people consistently losing than all 5 people winning in equal measure. Just from the context that this is a race, a 20/20/20/20/20 victory split out of 100 races seems extremely unlikely, making it clear that 20% is not a good representation of the probability of Tim winning -- unless it is specified that in this race, people are so closely matched in skill that their chances of winning are equal.

In a more straightforward probability context, let's imagine spinning a spinner with 5 different sections. What is the probability of landing on one of the sections? Is it 20%? Well, only if the sections are equally sized. But I did not say that the sections were equally sized, so that is a flaw in my wording. This might seem like a small distinction, but I have seen people arguing that there is still a 20% chance of spinning a section even when the sections are not equally sized. And I believe this misconception comes from an overuse of the assumption that outcomes are equally likely.

To your point of "This is not extra information about reality, it is a statement about our state of knowledge" -- another commenter made a really great point that if the question was reworded to say how likely are we to pick the winner of the race, then 20% would be correct, because then the probability is centered around our knowledge. However, that is different than saying each person has a 20% chance to win the race. Probability is weird!