In the Standard Model of particle physics, the strength of the couplings of the \(b\) quark to the \(u\) and \(c\) quarks, \(|V_{ub}|\) and \(|V_{cb}|\), are governed by the coupling of the quarks to the Higgs boson. Using data from the LHCb experiment at the Large Hadron Collider, the probability for the \(\Lambda^0_b\) baryon to decay into the \(p \mu^- \overline{\nu}_\mu\) final state relative to the \(\Lambda^+_c \mu^- \overline{\nu}_\mu\) final state is measured. Combined with theoretical calculations of the strong interaction and a previously measured value of \(|V_{cb}|\), the first \(|V_{ub}|\) measurement to use a baryonic decay is performed. This measurement is consistent with previous determinations of \(|V_{ub}|\) using \(B\) meson decays to specific final states and confirms the existing incompatibility with those using an inclusive sample of final states.