To prove that if $(S, d)$ is a metric space, $p \in S$ and $X_n$ are random variables on a probability space $(\Omega, A, P)$ such that the law of $X_n$ converges weakly to $δ_p$, then $X_n \to p$ in probability.
Here $\delta_p(S) = \begin{cases} 1 & \text{if } p \in S \\ 0 & \text{otherwise} \end{cases}$.
Require some hints to proceed with the problem.