  Recently a peak structure was observed near the $K^{-} p p$ threshold in the
in-flight ${}^{3} {\rm He} (K^{-} , \, \Lambda p) n$ reaction of the E15
experiment at J-PARC, which could be a signal of a $\bar{K} N N$ bound state.
In order to investigate what is the origin of this peak, we calculate the cross
section of this reaction, in particular based on the scenario that the $\bar{K}
N N$ bound state is indeed generated and decays into $\Lambda p$. We find that
the numerical result of the $\Lambda p$ invariant-mass spectrum in the $\bar{K}
N N$ bound scenario is consistent with the J-PARC E15 data.
