The data sample of Λ0b→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 Λ0b→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.