Hi, I'm not sure what the notation is supposed to mean in the highlighted box and how it relates to conditional probability:

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The definition of conditional probability that I'm familiar with is P(A|B) = P(A, B)/P(B). How (if at all) does that relate to what the authors have written there? Some special properties of the normal distribution perhaps?

PS. Theta is a vector of reals, as is x, so $\displaystyle \theta^Tx^{(i)}=\theta\cdot x^{(i)}$