  The data sample of $\Lambda_b^0\to J/\psi p K^-$ 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 $J/\psi p$ or
$J/\psi K^-$ contributions with minimal assumptions about $K^- p$
contributions. It is demonstrated at more than 9 standard deviations that
$\Lambda_b^0\to J/\psi p K^-$ decays cannot be described with $K^- p$
contributions alone, and that $J/\psi p$ contributions play a dominant role in
this incompatibility. These model-independent results support the previously
obtained model-dependent evidence for $P_c^+\to J/\psi p$ charmonium-pentaquark
states in the same data sample.
