Ants on a Triangle Puzzle Solution

Well let's see all the possibilities of this puzzle. there are total 8 possibilities for this puzzle in which the ants can move. Let us assume a triangle ABC. So the 8 combinations will be

1.  A->B, B->C, C->A
2.  A->B, B->A, C->A
3.  A->B, B->A, C->B
4.  A->B, B->C, C->B
5.  A->C, B->C, C->A
6.  A->C, B->A, C->A
7.  A->C, B->A, C->B
8.  A->C, B->C, C->B

So in these 8 possibilities there will be two non colliding movements
1 and 6.

So the probability will be 2/8 = 0.25.