If $X$ is a covering space of $Y$ with the covering map $p$ and $Y$ is connected, then $p^{-1}(y)$ have the same cardinality for every $y\in Y$.
If $h : Y \to X$ is a covering map and $Y$ is connected, then the cardinality of the fiber $h^{-1}(x)$ is independent of $x \in X$.