  We perform a theoretical analysis of the $\Lambda_b \to J/\psi K^- p$
reaction from where a recent LHCb experiment extracts a $\Lambda(1405)$
contribution in the $K^- p$ spectrum close to threshold and two baryon states
of hidden charm in the $J/\psi\,p$ spectrum. We recall that baryon states of
this type have been theoretically predicted matching the mass, width and $J^P$
of the experiment, concretely some states built up from the $J/\psi\, N$, $\bar
D^* \Lambda_c$, $\bar D^* \Sigma_c$, $\bar D \Sigma^*_c$ and $\bar D^*
\Sigma^*_c$ coupled channels. We assume that the observed narrow state around
4450 MeV has this nature and we are able to describe simultaneously the shapes
and relative strength of the the $K^- p$ mass distribution close to threshold
and the peak of the $J/\psi\,p$ distribution, with values of the $J/\psi\, p$
coupling to the resonance in line with the theoretical ones. The non trivial
matching of many properties gives support to a $J^P=3/2^-$ assignment to this
state and to its nature as a molecular state mostly made of $\bar D^* \Sigma_c$
and $\bar D^* \Sigma^*_c$.
