I have multiple stochastic processes that can have 2 different realisations. I think of them as coins that can take the values heads or tails. For the example I assume that there are 3 coins. I know the 3 probabilities of showing heads that these coins have, but I don't know which belongs to which coin. For example I know that the probabilities are 60%, 50%, and 40% and each occurs exactly once i.e. if Coin A has a probability of 60% for heads, Coin B and C cannot have 60%.
I observe realisations for each coin over multiple rounds. With 3 coins there are 3! = 6 different ways the probabilities could be assigned to the coins. For each of these 6 possibilities I want to know probability that it is the true one given the data on the realisations of the 3 coins that I have. For example I want a result like with 20% probability Coin A has 60% probability of heads, Coin B has 50% and Coin C has 40% and with 15% Probability Coin A has 50% probability of heads, Coin B has 60% and Coin C has 40% and so on.
How can I calculate these probabilities?