Let $\Pi:X\to S$ be a fibred surface, i.e., $X,B$ are integral regular complete schemes of respective dimensions 2 and 1.
Let $\operatorname{Num}(X)$ be the quotient of $\operatorname{Pic}(X)$ by the subgroup consisting of iso classes of invertible sheaves numerically equivalent to $0$.
Claim: The image in $\operatorname{Num}(X)$ of a closed fiber $X_b \hookrightarrow X$ of $\Pi$ is independent of $b\in B(k)$.
I struggle to see why the claim is true even knowing that the numerically equivalent to zero divisors are the ones with intersection number zero with any divisor.
Thank you for your help.