Hmm, I think when the author gets to imagining an "infinite dataframe" to deal with conditioning with continuous variables, it's kind of revealed that this isn't the best way to build intuition. Worse, sometimes we talk about conditioning on _unobserved_ variables which wouldn't be in your dataframe. This happens when we describe a model with latent/hidden variables that impact the stuff we do observe.

I think a conventional way of describing this, which I think is in intro textbooks, is better -- we thinking of cutting slice through a multivariate distribution, and then normalizing. If you have some distribution P(X, Y) where X and Y are both real, then its density is like some landscape (i.e. each x,y is associated with some height). P(X | Y=y) is like a slice through that landscape at Y=y, which leaves a 1-D plot of the density along X. If we re-scale it so that the area under it is 1, then it's a well-formed PDF.