A search is performed for the charmless three-body decays of the Λ b 0 and Ξ b 0 baryons to the final states Λh + h′−, where h (′) = π or K. The analysis is based on a data sample, corresponding to an integrated luminosity of 3 fb−1 of pp collisions, collected by the LHCb experiment. The Λ b 0  → ΛK +π− and Λ b 0  → ΛK + K − decays are observed for the first time and their branching fractions and CP asymmetry parameters are measured. Evidence is seen for the Λ b 0  → Λπ+π− decay and limits are set on the branching fractions of Ξ b 0 baryon decays to the Λh + h′− final states.