538 derives their probabilities by running simulated elections.
http://fivethirtyeight.blogs.nytimes.com/methodology/Somewhat intuitively, the simulations themselves have concepts of "national movements", where a candidate can (with some probability) gain 1%, 2%, etc. across all states.
The state probabilities are then derived from how many simulations/total candidate A won. However, partly because these simulations actually had national movement effects, you'll find that odds of winning both Florida and Ohio (as in # simulations/total candidate A wins both states) are not the state odds multiplied (they odds actually should be higher).
That said, with the raw simulation data, the graphic could show probabilities for every combination.