"I got lost here (and in the following equations..."

A causal model goes beyond the graph by including specific probability functions $\\mathbb P(X\_i | \\mathbf{pa}\_i)$ for how to calculate the probability of each node $X\_i$ taking on the value $x\_i$ given the values $\\mathbf {pa}\_i$ of $x\_i$'s immediate ancestors\. It is implicitly assumed that the causal model factorizes, so that the probability of any value assignment $\\mathbf x$ to the whole graph can be calculated using the product:

I got lost here (and in the following equations). I think it's a combination of needing the "factorizes" redlink filled in, and not understanding the do() syntax.