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Hello, I'm Dr. Deb and will do my best to help with this concern about your son's dog.
As strange as it may sound, dogs will often engage in this behavior. It can be a way of gathering information about the the other dog since their sense of smell is quite acute and they often are detecting chemicals which aren't at all obvious to us. It can be a way of getting to know the other dog although I know this may sound odd.
If this is relatively new behavior, though, and they've been around each other before and your son's dog hasn't gone to an extreme in sniffing this area of your dog, then I'd want to check out your dog's anal glands. It's possible that there's a small amount of discharge from these glands that the other dog is detecting and is interested in this "new" smell. If you're not familiar with anal glands in dogs, the following link provides more information about these glands:
In other words, I wouldn't consider this to be particularly abnormal behavior from a dog's perspective but I probably would want to ensure that your dog's anal glands are emptying as they should when he has a bowel movement.
I hope this helps, Deb