Three-body B+ → ppK+ and B(+) → ppπ(+) decays are studied using a data sample corresponding to an integrated luminosity of 3.0 fb(-1) collected by the LHCb experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV. Evidence of CP violation in the B(+) → ppK(+) decay is found in regions of the phase space, representing the first measurement of this kind for a final state containing baryons. Measurements of the forward-backward asymmetry of the light meson in the pp rest frame yield A(FB)(ppK(+),m(pp)<2.85 GeV/c(2)) = 0.495 ± 0.012 (stat) ± 0.007 (syst) and A(FB)(ppπ(+),m(pp) <2.85 GeV/c(2)) = -0.409 ± 0.033 (stat) ± 0.006 (syst). In addition, the branching fraction of the decay B(+) → Λ(1520)p is measured to be B(B(+) → Λ(1520)p) = (3.15 ± 0.48 (stat) ± 0.07 (syst) ± 0.26 (BF)) × 10(-7), where BF denotes the uncertainty on secondary branching fractions.