is the probability limit of $\frac{X}{n}$ just $0$?

Question

let's say $X_n \sim B(n,p)$ assuming i.i.d conditions check then by the law of large numbers $\frac{X_n}{n}$ converges in probability to $p$

now let's say $X \sim B(a,p)$ where $a$ is a large but fixed number, then does $\frac{X}{n}$ converges in probability to $0$ ?

Answer 1

It converges a.s. to $0$, so obviously, in probability as well.