So I have been given the following details:
$p(a\mid b)=0.2\\ p(a\mid \lnot b)= 0.6$
How would I use this to determine $p(\lnot a\mid b)$? Is there some kind of a formula/procedure I can use or is there incomplete information?
I don't think that $p(\lnot a\mid b)= 1-p(a\mid b)$, but I can't think of any other ways
Once you draw the probability tree and let P(b)=x, it will become clear to you.
Given b, either a or (not a) will happen for sure. Thus, $P(a|b)+P(not\; a|b)=1$ for sure.