I am quite confused about the following situation: suppose that we have a map $f \colon X \to Y$. Its homotopy fibre is defined as the pullback of the following of diagram:
\begin{matrix} Ff & {\rightarrow} & * \\ \downarrow{} && \downarrow{} \\ X & \rightarrow{} & Y \end{matrix}
Now if $g \colon W \to Z$ is another map and the diagram \begin{matrix} W & {\rightarrow} & X \\ \downarrow{} && \downarrow{} \\ Z & {\rightarrow} & Y \end{matrix}
is homotopy cartesian, why does it follow that the homotopy fibres of $f$ and $g$ are weakly equivalent?