These probabilities are not required to sum to 1, because they are not incompatible and exhaustive possible outcomes of an experiment. More obvious example to illustrate:
P(6-sided die coming up as 6 | today is Monday) = 1/6
P(6-sided die coming up as 6 | today is not Monday) = 1/6
1/6 + 1/6 != 1
I think your example is not suitable for situation above - there I can see only two possible outcomes: X happen or X not happen. We don't know anything more about X. And P(X|A) + P(X|~A) = 1, isn't so?
Another month has passed and here is a new rationality quotes thread. The usual rules are: