Informational Content:A signal r carries the information that s is F = The conditional probability of s's being F, given r (and k), is 1 (but, given k alone, less than 1)This is what I think he is saying.
The equals sign is saying that what comes on the right is the definition for what is on the left. That is, what is on the right is the condition under which we can say that a signal r carries the information that s is F.
This condition is a follows.
P(s=F|r and k) = 1
P(s=F|k and (r not received)) < 1