In definition 2.2 of nlab we define the homotopy fiber
Let $f:X \rightarrow Y$ be a morphism in a model category $C$, its homotopy fiber $$hofib(f) \rightarrow X $$ is given by the morphism in $Ho(C)$ represented by the fiber of any fibrant resolution.
This is confusing to me, given a fibrant resolution $$ f:X \xrightarrow{\in W} \hat{X} \xrightarrow{f' \in Fib} Y$$ Then we have $fib(f')$ being the fiber of $f'$ i.e. pullback along $* \rightarrow Y$ of $f'$. How does one obtain the morphism $$fib(f') \rightarrow X $$ in the homotopy category? We only have a map $fib(f') \rightarrow \hat{X}$. Do we post compose by the inverse of $X \xrightarrow{\in W} \hat{X}$?