We show how two-dimensional chemical shift conditional probability distributions can be extracted from experimental NMR correlation spectra of disordered solids. We show that transverse dephasing times are of central importance in determining the resolution (and sensitivity) of these probability distributions. These conditional probability distributions provide a new source of structural information characteristic of disordered solids, which is much more sensitive to structure than the individual-atom chemical shift distributions. The structural information contained in these distributions is clearly a potentially extremely rich source for understanding disorder. This is illustrated with examples of a phosphorus-containing organic compound and with a sample of disordered cellulose where the different structural allomorphs present are identified from the distributions.