lets say that $P(A|B) = X$
is true. Could something along the lines of
$P(A^c|B^c) = 1 - X$
, or maybe
$P(B^c|A^c) = X$
be said.
De Morgan's laws have been so useful and i was hoping they would extend further in probability, however i cannot find anything online
If I tell you that the shaded region is 60% of the Rhombus’s area, and ask you to talk about the areas of other regions, the only region you can talk about is the other 40%.
i.e In your case $P[B\cap A^c|B] = 1-X$ is all you can infer given the information at hand.
$\qquad$