At low temperatures the $4{f}^{2}$ configuration of ${\mathrm{Pr}}^{3+}$ in PrSb approaches a singlet-singlet system at the $X$ point as a result of the crystalline electric field and the anisotropy in the exchange. The energy of the longitudinal exciton decreases with applied pressure, and there is a transition at $T\ensuremath{\rightarrow}0\ifmmode^\circ\else\textdegree\fi{}$ from a Van Vleck paramagnet to an induced-moment antiferromagnet at ${P}_{c}=3.0\ifmmode\pm\else\textpm\fi{}0.2$ GPa. The magnetic structure, phase boundary, and magnetic moment have been determined, and they are in qualitative agreement with a molecular-field model for the transition. Near the critical pressure the longitudinal exciton softens with decreasing temperature and then saturates at a finite energy in the vicinity of the ordering temperature. RPA theories for the dynamics of the singlet-singlet model are not compatible with these results.