  We calculate the shape of the $\pi\Sigma$ and $\bar K N$ invariant mass
distributions in the $\Lambda_b \to J/\psi\, \pi\Sigma$ and $\Lambda_b \to
J/\psi \,\bar K N$ decays that are dominated by the $\Lambda(1405)$ resonance.
The weak interaction part is the same for both processes and the hadronization
into the different meson-baryon channels in the final state is related by SU(3)
symmetry. The most important feature is the implementation of the meson-baryon
final-state interaction using two chiral unitary models from different
theoretical groups. Both approaches give a good description of antikaon-nucleon
scattering data, the complex energy shift in kaonic hydrogen and the line
shapes of $\pi \Sigma K$ in photoproduction, based on the two-pole scenario for
the $\Lambda (1405)$. We find that this reaction reflects more the higher mass
pole and we make predictions of the line shapes and relative strength of the
meson-baryon distributions in the final state.
