Vanishing locus of global section of invertible sheaf has codimension one

Question

Let $X$ be a projective scheme over some field $k$. Let $\mathcal{L}$ be an ample invertible sheaf on $X$ and let $s \in \mathcal{L}(X)$ denote a global section of $\mathcal{L}$. Let $X_s = \{P \in X \mid s_P\mathcal{O}_{X,P} \cong \mathcal{L}_P\}$ be open. I am looking for a reference that $\operatorname{codim}(X\setminus X_s, X) \leq 1$ holds.