 for all \(A, B\) in \(\mathbf{A}\) where \(A \neq \varnothing\). We adopt the convention that \(\infty - \infty = 0\) and \(\infty - n = \infty\) for all finite \(n\). Note that this entails that \(\varrho(\neg A\mid A) = \infty\). Requiring that \(\varrho(\varnothing \mid B) = \infty\) for all \(B\) in \(\mathbf{A}\) guarantees that \(\varrho(\cdot\mid B)\) is a (non-conditional) ranking function. Conditional ranking functions give rise to a ranking-theoretic counterpart of strict conditionalization: