Clarification of Conditional Probability Interpretation

[tushar]

Let's say x is determined by a normal distribution and p(y|x) is a sigmoid function if y = 1 and the sigmoid reflected along the vertical axis if y = -1.

p(y|x) = {
f(x) if y = 1
1 - f(x) if y = -1
}

Then p(x, y) = p(y|x) * p(x)

So for the case y = 1, does it make sense to say that p(x, y) is just the multiple of the sigmoid function and the normal distribution?