I was reading a book on group and representation theory and came across the following which I don't understand, I'd appreciate any help.
Suppose P and Q are probabilities on a finite group G. Thus $P(s)\ge0$ and $\sum_s P(s)=1$. By the convolution $P*Q$ we mean the probability $P*Q(s)=\sum_t P(st^{-1})Q(t)$; "first pick $t$ from $Q$, then independently pick $u$ from $P$ and form the product $ut.$" Note that in general $P*Q \ne Q*P$.
EDIT: the first line is standard, but the latter I cant figure.