Wikipedia defines convergence in probability as

A sequence ${X_n}$ of random variables converges in probability towards the random variable $X$ if for all ε > 0 $$\lim_{n\rightarrow\infty} P(|X_n-X|>\varepsilon) = 0$$

I wonder why the limit $X$ is a random variable. I think $X$ as a r.v. can only be a constant, and defining convergence to a number $a$ instead of a r.v. $X$

$$\lim_{n\rightarrow\infty} P(|X_n-a|>\varepsilon) = 0$$

makes the definition more clear.