  Two observations are in order: first, in the case of certainty that if \(A\), \(B\), provided that \(A\) does not have probability 0, degree of belief in the material conditional and the conditional degree of belief in \(B\) given \(A\) coincide. Writing “\(\bel\)” for degree of belief: if \(\bel(A \amp \neg B\)) = 0 but \(\bel(A) \neq 0\), both \(\bel(A \supset B) = 1\) and \(\bel(B \given A) = 1.\) The only other case in which they coincide is if \(\bel(A) = 1.\) Otherwise, \(\bel(A \supset B) \gt \bel(B \given A),\) radically so when \(\bel(B \given A)\) is low but \(\bel(\neg A)\) is high. Second, it is clear that Ramsey does not reductively define conditional degree of belief in terms of the ratio: \(\bel(A \amp B)/\bel(A),\) for the conditional degree of belief can be assessed even without any specific value for \(\bel(A).\) Indeed, in the fundamental law stated above, the right-hand side is much more use as a route to the probability of a conjunction, rather than the other way round.