P(A)=1/4 = P(A/B) That means A and B are independent events. Whether B happens or not P(A) remains 1/4=0.25. P(A)=P(A/B)=P(A/~B)=1/4 P(A) might be a baseball player's probability of getting a hit, his batting average: .250 Event B could be the event of his wife being home after the game. They're unrelated, independent events.
Since they're unrelated, it works both ways: P(B)=P(B/A)=.4=P(B/~A)
IF A and B are independent events, so are not A and not B:
P(~A/~B)=P(~A)= 1-P(A)=1-.25=0.75 = 3/4 and similarly
P(~B/~A)=P(~B)=P(~B/A)=1-P(B) If P(B)=.4 given in part (a) as well as implicitly in the initial problem, then P(~B)=1-.4=.6 = P(~B/~A)