"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.