What is the probability that the ants don't collide?

There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.

What is the probability that they don't collide?


Let's mark the corners of the triangle as A,B,C. There are total 8 ways in which ants can move.
1. A->B, B->C, C->A
2. A->B, B->C, C->B
3. A->B, B->A, C->A
4. A->B, B->A, C->B
5. A->C, C->B, B->A
6. A->C, C->B, B->C
7. A->C, C->A, B->Ajavascript:void(0)
8. A->C, C->A, B->C

Out of which, there are only two cases under which the ants won't collide :
 A->B, B->C, C->A
 A->C, C->B, B->A

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