Studies of charmless three-body decays of the Ξb ̅ and ꭥb baryons to ph-h'- final states, where h(') denotes a kaon or pion, are presented. The first part of the analysis is based on a sample of proton-proton collision data collected by the LHCb experiment at centre-of-mass energies √s = 7 & 8TeV, corresponding to an integrated luminosity of 3 fb-1. In this analysis, the decay Ξb ̅→ pK-K- is observed with a significance of 8:7 standard deviations, and evidence at the level of 3:4 standard deviations is found for the Ξb ̅→pK-π- decay. The results are reported, relative to the B-→K+K-K- normalisation channel, for the products of branching fractions and b-hadron production fractions. The branching fractions of Ξb ̅→pK-π- and Ξb ̅→pK-K- relative to of Ξb ̅→pK-K- decays are also measured. In the second part of the analysis, an amplitude analysis of Ξb ̅→pK-K- decays is presented. This analysis is based on a data sample corresponding to integrated luminosities of 1 fb-1, 2 fb-1, 0:3 fb-1 and 1:7 fb-1 collected by LHCb during 2011 (√s = 7TeV), 2012 (√s = 8TeV), 2015 (√s = 13TeV) and 2016 (√s = 13TeV) respectively. Sensitivity to the CP violation parameters in Ξb ̅→ pK-K- decays is also presented. An updated search for the previously unobserved charmless decay ꭥb ̅→ pK- K- is also conducted.