The recently developed conditional probability density functional theory (CP-DFT) yields direct access to the exchange-correlation hole of a system, an important correlation function that is not available in standard DFT. We present the first results for extended materials with periodic boundary conditions. We validate CP-DFT for weakly correlated Na and Si. We apply it to a stretched hydrogen chain, the prototype of strong correlation. When applied to the Kagome material CsV${}_3$Sb${}_5$, we find $d$-orbital correlations that are missing in standard DFT, implying an enhanced finding probability between two separated electrons and a local charge density wave related modulation.