What I'm saying is that there is a lower probability that someone in 1500 married a non-descendant of Edward III than 20000 / 4million
But it is not THAT much lower. Say, for argument's sake, as many as half those descendants classed themselves as nobility and never married outside their "class", and demanded that all their descendants did likewise. That leaves 10,000 to mix with the rest of society (of whom many had already done so).
So, it's now only a 35 to 1 chance that you are NOT descended from Edward III.
Statistics throws up some non-intuitive truths. For example, how many people do there have to be in a room for it to be more likely than not that two of them share the same birthday? The answer is just 23. If there are 70 people, the chances of a match of birthday are 99.9%. Statistics are not just a mathematical concept - bookmakers make a good living out of them.