I am learning about abstract homotopy theory and know that when $Y$ is fibrant then right homotopy is an equivalence relation on the set of maps from $X$ to $Y$. When $Y$ isn’t, then transitivity might fail. I am trying to find an example where this is the case in the Kan-Quillen model structure on simplicial sets. I know that for this, I have to find objects that aren’t fibrant and since I’m working in the Kan-Quillen model structure, this corresponds to $Y$s that aren’t Kan complexes. I was thinking about using $\Delta[n]$ but I am stuck finding an $X$ and maps $X\to Y$ such that transitivity fails.
Any help is appreciated!