Statistics Probability Question

Suppost that A1, A2, A3 and B are events where A1, A2, A3 are mutally exclusive and
P(A1)=.2
P(A2)=.5
P(A3)=.3
P(B|A1) = .02
P(B|A2)=.05
P(B|A3)=.04

use this information to fine P(A1|B), P(A2|B), P(A3|B)

How do I figure out this problem? The book is pretty useless....I have the answers, I need to know how to do it....thanks

P(A1 & B) = P(A1).P(B|A1) = .2*.02 = .004,
P(B) = P(B|A1) + P(B|A2) + P(B|A3) = .11

P(A1|B) = P(A1 & B) / P(B) = .004/.11 = 2/55 <---------

work others out in exactly the same way