Suppose we have two infinite sets $A$ and $B$ such that $|A|>|B|$. And let $C=A\cup B$.
Assume that $P(x)$ is the probability of selecting an element $x, \forall x \in C$ following the uniform distribution.
Is it true that:
$$P(x_a\mid x_a \in A) \;>\; P(x_b \mid x_b \in B)$$