Let $f:Y\rightarrow X$ be a proper birational morphism. Suppose that $X$ is normal and $Y$ is smooth. Let us write the largest open subset U of X such that $f^{-1}$ can be defined.

I want to show that $\operatorname{codim}(X\backslash U)\geq2$.

I think that I should use Zariski's main theorem but I don't know how to use. Thank you.