Solution
Consider the triangle ABC. We assume that the ants move towards different corners along the edges of the triangle.
Total no. of movements: 8
A->B, B->C, C->A
A->B, B->A, C->A
A->B, B->A, C->B
A->B, B->C, C->B
A->C, B->C, C->A
A->C, B->A, C->A
A->C, B->A, C->B
A->C, B->C, C->B
Non-colliding movements: 2
A->B, B->C, C->A
A->C, B->A, C->B
(i.e. the all ants move either in the clockwise or anti-clockwise direction at the same time)
P(not colliding) = 2/8 = 1/4 = 0.25