A probabilistic analysis of the generation of dual site-bond models for the energy landscape of adsorbents is presented, focusing attention on the self-consistent case. To generate an uncorrelated site-bond energy landscape with prescribed distribution functions F-S(*)(E) and F-B(*)(E) consistent with the two basic laws of the dual site-bond model, the random variables associated with the site and bond energies should possess the Local distribution functions Fs(E) and F-B(E), which are related to F-S(*)(E) and F-B(*)(E) through a nonlinear integral equation. In particular, the inverse problem in two dimensions is solved in closed form. The analytical solution for the inverse problem provides a clear description of the intrinsic correlation in the energy landscape induced by the fulfillment of the construction principle.