Dog "bully" - dog smells at another dog's rear

Last night when I was talking a walk, a guy was with his small dog talking a walk too. Ahead of us there were two large dogs laying on the ground resting. When the walking dude and his dog passed the other two dogs, one of the larger dog suddenly jumped up and chased the smaller dog all over the place. When he caught up with the smaller dog (less than 1/5 of his size), the larger dog put his nose against the smaller dog's rear.

I am not exactly sure the gender of those dogs, because it was quite dark. They are different breeds for sure. The smaller dog had white fur, the larger dog had black fur.

What was he doing?