Fibrant objects of marked simplicial sets

Question

Im reading the nlab article one the Cartesian model structure on the category of marked simplicial sets over a simplicial set $S$. Here it is stated just below Proposition 3.1 which is a characterization of the fibrant objects. It says that a marked simplicial sets $X$ is fibrant if and only if $X \simeq Y$, where $Y \to S$ is a Cartesian fibration. The case $S=\Delta^0$, shows that the fibrant objects of $sSet^+$ are the $\infty$-categories, where the marked edges are the equivalences. I can't see why this is true. I have also tried to read the corresponding part in HTT, but it didn't help me.