Each ant can run in clockwise or in an Anti-clockwise direction. So there can be 8 possible ways in which they can start running. They will not collide only if all 3 run in either clockwise or in an Anti-clockwise direction.
So the required probability is 2/8 = 1/4.
An after thought - this holds good only if the ants run with the same speed otherwise the ants will collide.