 Yet it can be proved (with elementary probability theory) that \(\Cr_\textrm{new}\) cannot be obtained from \(\Cr_\textrm{old}\) by a Jeffrey conditionalization on \(\textsf{red}\) (assuming the two conditions \((a)\) and \((b)\) in the above case, the Ratio Formula, and that \(\Cr_\textrm{old}\) is probabilistic). See  supplement H  for a sketch of proof.