The Ants on a Triangle

Problem

Three ants are placed at the three vertices of an equilateral triangle. At a given signal, each ant independently and randomly chooses one of two directions -- clockwise or counterclockwise -- each with equal probability 1/2. Then all three ants simultaneously begin walking along the edges of the triangle at the same speed.

If two ants are ever at the same point on an edge while traveling in opposite directions, they collide.

What is the probability that no two ants collide?