A locally lowered surface potential develops around potassium atoms on a transition metal surface. These potentials are accessible experimentally by measuring the ultraviolet photoemission spectra of adsorbed noble gases. We determine the potassium-induced change in electrostatic potential on K/Rh clusters on the basis of calculated electronic structures using density functional theory. It appears that the calculated potentials depend critically on the geometry of the cluster and may differ substantially from the experimentally observed values. Clusters that allow a substantial charge redistribution around the potassium atoms give the best results. Another improvement is obtained from adding the contribution of potassium atoms further away from the potential. We also present theoretical evidence that the potassium-induced change in ionization energy of Xe, Kr, and Ar on a Rh15K3 cluster is mainly determined by the change in electrostatic potential. This provides support for the use of photoemission of adsorbed noble gases as a probe for changes in local surface potential induced by adsorbed species.