The probability in GP's comment assumes that everyone has an equal chance of attaining billionaire status, and that the percentage of billionaires in the world remains constant. Given heritability of wealth and access to better education and healthcare, wealthy children have much lower barriers to success. The second assumption may not hold either, as the current overall economic trends seem to favor increasing concentration of wealth.
It'd be interesting to see just how steeply those advantages decrease the odds for the rest of us. I'd be willing to bet that—even in a comparatively wealthy developed country—the true chances for an average person achieving >$1B are orders of magnitude lower than the figure quoted.