If an experiment is conducted, one and only one of three mutually exclusive events S1, S2, and

Question:

If an experiment is conducted, one and only one of three mutually exclusive events S1, S2, and S3 can occur, with these probabilities:
P(S1) = .2 P(S2) = .5 P(S3) = .3
The probabilities of a fourth event A occurring, given that event S1, S2, or S3 occurs, are
P(A | S1) = .2 P(A | S2) = .1 P(A | S3) = .3
If event A is observed, find P(S1 | A), P(S2 | A), and P(S3 | A).