Consider identical looking four coins labeled as C1, C2, C3 and C4.

C1 is unbiased and, the probability of getting heads in a toss is 1/2.
C2 is biased and, the probability of getting heads in a toss is 3/4.
C3 is biased and, the probability of getting heads in a toss is 5/6.
C4 is biased and, the probability of getting heads in a toss is 7/8.

Exactly one of the coins is chosen at random with equal probability. The chosen coin is tossed nine times and the outcome is: HHHHHTTTT.

Determine the probability that the chosen coin is C1. What is the probability that the chosen coin is C4?