Let $X_1$, $X_2$, ..., $X_n$ be independent normal variables with zero mean and decreasing variances: $X_i=N(0,v_i)$ where $v_1>v_2>...>v_n\ge 0$. Assume $n>2$. Let $p_i=Prob(X_i = max(X_1,X_2,...,X_n))$.
Prove the following
Conjecture: $p_1>p_2>...>p_n$.