The solubility of noble gases and water in molten salts is predicted by developing an analytical parameter-free description in terms of polarizable hard sphere (the gas particle) in a medium composed of charged hard spheres of comparable size (the salt). The chemical potential of solute contains contributions from excluded volume, polarization, and dispersion forces. The polarization of the gas particle is calculated explicitly within the framework of the mean spherical approximation for the ion-dipole mixture. An additional contribution originating from the polarization of the salt is proposed. This effect has been overlooked in previous theoretical studies. Its magnitude is estimated in an approximate way. The description is found to give predictions that are in good agreement with experimental solubility data for noble gases and water in molten KCl and RbCl. The results suggest that volume exclusion and salt polarization may constitute the main two opposing factors affecting this phenomenon.