Is this statement correct? If $X_n \xrightarrow{a.s} c$, where $X_n$ is a sequence of random variables and $c$ is a constant, then we can conclude that since almost sure convergence implies on convergence in distribution
$$X_n \xrightarrow{d} c$$
Therefore,
$\lim\limits_{n \to \infty} P(X_n<t)=\lim\limits_{n \to \infty} P(c<t) = \begin{cases} 1 & c< t\\ 0 & c \geq t\end{cases}$