Almost everywhere we look, we find empty lattice cells. Nevertheless, we do find molecules in a few occupied cells. When there is real mixing, for each of those few occupied cells, there is a contingent uncertainty about which kind of molecule it is. When there is no real mixing because the two substances are identical, there is no uncertainty about which kind of molecule it is. Using conditional probabilities, it turns out that the analytical problem for the small subset of occupied cells is exactly the same as for mixed liquids, and the "increase" in the entropy, or spatial uncertainty, has exactly the same form as obtained previously. Obviously the subset of occupied cells is not the same at different times. But only when there is real mixing and an occupied cell is found do we ask which kind of molecule is there.