Assume $X_{n}$ is a sequence of random variables taking values from some finite discrete space. Next, assume $$ P(X_{n} = c) \to 1, $$ for some $c$, as $n \to \infty$.
I would like to find an example of a sequence $X_{n}$, such that $$ X_{n} \overset{a.s.}{\not\to} c $$ i.e. the convergence a.s. does not hold.
