We say that a Sequence of Random variables $(X_n)_{n\in \mathbb{N}}$ converges in probability to random variable $X$, if:

For any $\epsilon > 0$, $\delta > 0$

there exists a sufficiently large $n_0$ such that

For all $n>n_0$

$\text{Pr}\left[|X_n - X| > \epsilon\right] < \delta$

Remember that the random variables may not be "random". I.e. a deterministic value is a particular case of a random variable in the technical sense.