Suppose that \(k\) events \(B_1\), \(B_2\), …, \(B_k\) form a partition of the sample space \(S\), and \(A\subseteq S\) is some event with positive probability \(P(A)>0\). Show that if \(P(B_1\mid A)<P(B_1)\), then that guarantees \(P(B_i\mid A)>P(B_i)\) for at least one \(i\in\{1,\,2,\,...,\,k\}\).