  There may exist seven $\bar D^{(*)} \Sigma_c^{(*)}$ hadronic molecular
states. We construct their corresponding interpolating currents, and calculate
their masses and decay constants using QCD sum rules. Based on these results,
we calculate their relative production rates in $\Lambda_b^0$ decays through
the current algebra, i.e., $\mathcal{B}(\Lambda_b^0 \to P_c
K^-):\mathcal{B}(\Lambda_b^0 \to P_c^\prime K^-)$ with $P_c$ and $P_c^\prime$
two different states. We also study their decay properties through the Fierz
rearrangement, and further calculate these ratios in the $J/\psi p$ mass
spectrum, i.e., $\mathcal{B}(\Lambda_b^0 \to P_c K^- \to J/\psi p
K^-):\mathcal{B}(\Lambda_b^0 \to P_c^\prime K^- \to J/\psi p K^-)$. Our results
suggest that the $\bar D^{*} \Sigma_c^{*}$ molecular states of $J^P = 1/2^-$
and $3/2^-$ are possible to be observed in future experiments.
