Two identical robots on a loop that must meet

Two identical robots are dropped on different stations of a circular track with $n$ stations. They run the exact same program. Each second, a robot may step one station clockwise, step one station counterclockwise, or stay put, and both act at the same instant. They want to guarantee they will one day both sit on the same station at the same second.

First: show that no fixed (deterministic) identical program can guarantee a meeting. Then: give a plan that succeeds with probability 1.