  The interaction of $\rm{K}^{-}$ with protons is characterised by the presence
of several coupled channels, systems like ${\rm \overline{K}^0}$n and
$\pi\Sigma$ with a similar mass and the same quantum numbers as the
$\rm{K}^{-}$p state. The strengths of these couplings to the $\rm{K}^{-}$p
system are of crucial importance for the understanding of the nature of the
$\Lambda(1405)$ resonance and of the attractive $\rm{K}^{-}$p strong
interaction. In this article, we present measurements of the $\rm{K}^{-}$p
correlation functions in relative momentum space obtained in pp collisions at
$\sqrt{s}~=~13$ TeV, in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeV,
and (semi)peripheral Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeV.
The emitting source size, composed of a core radius anchored to the
$\rm{K}^{+}$p correlation and of a resonance halo specific to each particle
pair, varies between 1 and 2 fm in these collision systems. The strength and
the effects of the ${\rm \overline{K}^0}$n and $\pi\Sigma$ inelastic channels
on the measured $\rm{K}^{-}$p correlation function are investigated in the
different colliding systems by comparing the data with state-of-the-art models
of chiral potentials. A novel approach to determine the conversion weights
$\omega$, necessary to quantify the amount of produced inelastic channels in
the correlation function, is presented. In this method, particle yields are
estimated from thermal model predictions, and their kinematic distribution from
blast-wave fits to measured data. The comparison of chiral potentials to the
measured $\rm{K}^{-}$p interaction indicates that, while the
$\pi\Sigma-\rm{K}^{-}$p dynamics is well reproduced by the model, the coupling
to the ${\rm \overline{K}^0}$n channel in the model is currently
underestimated.
