This is a very complicated problem. Just try counting ancestors.

You have 2 parents, 4 grandparents, 8 great grandparents, ... So if you go back $n$ generations then you have $2^n$ ancestors. Let's assume an average generation length of $25$ years. Then there have been about $28$ generations since 1300, which gives us about 268 billion ancestors at that time.

There is nowhere near that many people on Earth now or then. Which means there must have been a significant amount of intermarriage within your family tree, e.g. cousins marrying.

What happens when you try counting ancestors?

You have 2 parents, 4 grandparents, 8 great grandparents, ... So if you go back $n$ generations then you have $2^n$ ancestors. Let's assume an average generation length of $25$ years. Then there have been about $28$ generations since 1300, which gives us about 268 million ancestors at that time.

This is the right ballpark, but there is something wrong with this calculation, because the population of Earth in 1300 did not mix uniformly, and we are ignoring intermarriage within your ancestral "tree", i.e. we are double counting some ancestors.

Still, I think, this can lead to a correct upper bound on the probability that randomly chosen person in 1300 is your ancestor by taking the ratio $2^{28}$ to the population in 1300