Chapter 4, Problem 4.10P

Let X be the winnings of a gambler. Let $p\left(i\right)=P\left(X=i\right)$ and suppose that $\begin{array}{l}p\left(0\right)=\frac{1}{3};p\left(1\right)=p\left(-1\right)=\frac{13}{55}\\ p\left(2\right)=p\left(-2\right)=\frac{1}{11};p\left(3\right)=p\left(-3\right)=\frac{1}{165}\end{array}$

Compute the conditional probability that the gambler wins I, i = 1, 2, 3, given that he wins a positive amount.