[3JPLW]

They aren't independent. The developer of the 512 paths to the White House lamented this in getting conditional probabilities into the path choices. The simulations take into account the national popular vote polls and similar-state demographics (if one state goes one way, it's more likely that a similar one will, too).

Look at his EV histogram; 332 EVs had the highest probability of occurrence at nearly 20%. While there are other ways to get to 332, I'd imagine most of that percentage is from a map like last night. That's clearly not the partial probability of each state multiplied together.