We study the three-body Λb decays of Λb→J/ψpM with M=K− and π−. The two new states Pc1≡Pc(4380)+ and Pc2≡Pc(4450)+ observed recently as the resonances in the J/ψp invariant mass spectrum of Λb→J/ψpK− can be identified to consist of five quarks, uudcc¯, being consistent with the existence of the pentaquark states. We argue that, in the doubly charmful Λb decays of Λb→J/ψpK− through b→cc¯s, apart from those through the non-resonant Λb→pK− and resonant Λb→Λ⁎→pK− transitions, the third contribution with the non-factorizable effects is not the dominant part for the resonant Λb→K−Pc1,c2,Pc1,c2→J/ψp processes, such that we propose that the Pc1,c2 productions are mainly from the charmless Λb decays through b→u¯us, in which the cc¯ content in Pc1,c2 arises from the intrinsic charms within the Λb baryon. We hence predict the observables related to the branching ratios and the direct CP violating asymmetries to be B(Λb→π−(Pc1,c2→)J/ψp)/B(Λb→K−(Pc1,c2→)J/ψp)=0.58±0.05, ACP(Λb→π−(Pc1,c2→)J/ψp)=(−7.4±0.9)%, and ACP(Λb→K−(Pc1,c2→)J/ψp)=(+6.3±0.2)%, which can alleviate the inconsistency between the theoretical expectations from the three contributions in the doubly charmful Λb decays and the observed data.