Ancestry.ca has revealed that Justin Trudeau and Thomas Mulcair are cousins. Read all about it in this article at Global Genealogy. They are ninth cousins which means they have a pair of eight times great-grandparents in common.
We all have 1024 eight times great-grandparents. If each of those couples had three children, who each lived to have three children, and so on to the present generation, then each of the original 512 couples would have 19,683 eighth great-grandchildren. That's a total of over 10 million ninth cousins.
Not all families were that large. Pierre Trudeau was one of three siblings and had three sons, and a daughter out of wedlock. Many Quebec families were larger. Thomas Mulcair came from a family of ten children.
With four children at each generation there would be more than one hundred and thirty million ninth cousins.
Compare that to the current Quebec population of eight million.
A few smaller families,deaths, migration and cousin marriages accounts for the discrepancy. I'd be surprised if Trudeau and Mulcair were not more closely related than ninth cousin through lines not yet explored. If you know of a closer connection please post a comment.