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

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

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