Regarding the following question:
Find the probability that in a group of 20 individuals, there are at least 3 individuals born in March, given that there is an individual born in March 20.
The solution marks X as the number of individuals born in march and calculates: $$ P(X\geq3 | X \geq 1) $$
Claiming that X is binomial distributed. But why? What is the intuition for that? I though that binomial distribution mostly relates to experiments (like flipping a coin until "heads" shows etc), but for some reason this case doesn't look like an experiment or anything similar.
Thanks!