The third axiom of Probablity states that,
If $A_1,A_2,\ldots$ be a finite or infinite sequence of pairwise mutually exclusive events, then
$$P\left(\bigcup A_i\right)=\sum P(A_i)$$
We know that, $P\left(\bigcup A_i\right)\le 1$ but what guarantees that, $\sum P(A_i)\le 1$ for infinite case.
I am an beginner in this topic,so pardon me, if this question is a trivial one