The probability that after 1 minute that any
ant is where Alice started is zero.
You most probably got the question wrong or were told it wrong. If instead the circumference was 1m then the question would be interesting, as every second the ants would be in the same positions as when they started just permuted slightly.
The question was most probably taken fromhttp://gurmeet.net/puzzles/ants-in-a-circle/
which was incorrectly copied fromhttp://www.cs.cmu.edu/puzzle/puzzle9.html
which has a version of the question which makes sense and is interesting.
The site also outlines a solution.
Hope this helped,