I have discovered that I am related to someone specific who lived in 1066. How likely is this? In other words, the answer could be “No big deal. When you go back that many generations,the math shows that you are X percent likely to be related to anyone, where X is large - say 50-90% - because you have so many ancestors and the population then was so small.” Or the answer could be “WOW, that’s significant. Because the likelihood of that is small, where X is low.” So maybe the general question is “What is the likelihood that Person A, living now, is related to Person B, living in 1066?” And to specify even more narrowly, let’s constrain to the European/ Scandinavian/ Finnish populations that existed then.
I can say without a shadow of a doubt that you are "related to someone who lived in 1066", and to a very large number of people who were living in 1066.
Whether you are related to a particular person who was living in 1066 is very hard to prove, and at this point in time I think the best evidence that you will be able to muster are paper records that support every link in the lineage that you have assembled from that person to you.