This is a classic lateral thinking puzzle. If you overtake the person in first place, you take their position and become first. The key insight is that you must have been in second place to overtake the first-place runner.
If you overtake the runner who is currently in first place, you take over first place yourself — there's no one ahead of you anymore. This is a classic logic riddle designed to trip people up into thinking "second" simply because passing someone sounds like moving up rather than reaching the very top.