  Decays of beauty baryons to the $D^0 p h^-$ and $\Lambda_c^+ h^-$ final
states (where $h$ indicates a pion or a kaon) are studied using a data sample
of $pp$ collisions, corresponding to an integrated luminosity of 1.0 fb$^{-1}$,
collected by the LHCb detector. The Cabibbo-suppressed decays $\Lambda_b^0\to
D^0 p K^-$ and $\Lambda_b^0\to \Lambda_c^+ K^-$ are observed and their
branching fractions are measured with respect to the decays $\Lambda_b^0\to D^0
p \pi^-$ and $\Lambda_b^0\to \Lambda_c^+ \pi^-$. In addition, the first
observation is reported of the decay of the neutral beauty-strange baryon
$\Xi_b^0$ to the $D^0 p K^-$ final state, and a measurement of the $\Xi_b^0$
mass is performed. Evidence of the $\Xi_b^0\to \Lambda_c^+ K^-$ decay is also
reported.
