You are misunderstanding the outcome of logistic regression. A logistic regression will model $P(Y=1 | X)$. Thus since there are 2 classes, 0 and 1 for instance, this is what should sum to 1: $$ P(Y=1 | X) + P(Y=0|X) = 1 $$ And you can see that this is always true.

You are misunderstanding the outcome of logistic regression. A logistic regression will model $P(Y=1 | X)$. Thus since there are 2 classes, 0 and 1 for instance, this is what should sum to 1: $$ P(Y=1 | X) + P(Y=0|X) = 1 $$ And you can see that this is always true.

Note : the function cannot contains y's. So I am not sure of what is the formula that you wrote