The data sample of Λ_{b}^{0}→J/ψpK^{-} decays acquired with the LHCb detector from 7 and 8 TeV pp collisions, corresponding to an integrated luminosity of 3 fb^{-1}, is inspected for the presence of J/ψp or J/ψK^{-} contributions with minimal assumptions about K^{-}p contributions. It is demonstrated at more than nine standard deviations that Λ_{b}^{0}→J/ψpK^{-} decays cannot be described with K^{-}p contributions alone, and that J/ψp contributions play a dominant role in this incompatibility. These model-independent results support the previously obtained model-dependent evidence for P_{c}^{+}→J/ψp charmonium-pentaquark states in the same data sample.