Let \(S\) be a sample space with probability measure \(P\), and let \(B\subseteq S\) be some event with \(P(B)>0\). Show that the function \(G(A)=P(A\,|\, B)\) is a new probability measure on \(S\). That is, show that \(G\) satisfies the axioms:
- total measure 1;
- nonnegativity;
- countable additivity.