I got a few correct answer, the first one came from Akash Tayal from New Jersey. Well done! Am taking the liberty of reproducing his answer directly:

Out of total 8 permutations, There are 6 ways that the cap colors are split 2 of a kind and 1 of a kind. If the prisoners go with this bet, then anyone who sees 2 of the same color on the others’ head should guess the opposite color; the others should pass. 75% chance to be set. Also have put the answer on a video in more detail:

Hope you enjoyed the puzzle!