I'm looking to get some insight into a moderately challenging conditional probability problem:

Consider a sequence of random variables , ..., which each take the values 0 and 1. Assume that

Pr( = 1) = 1 - Pr( = 0) = , j =1,...,n

where 0 < < 1 and that

Pr( = 1| =1) = , j = 2,...,n.

(a) Find Pr( = 0| =1), Pr( = 1| =0),Pr( = 0| =0).

(b) Find the requirements on so that this describes a valid probability distribution for , ..., .

So for part (a) I have: 1- , , and 1- , respectively.

I do not know how to begin part (b).