Should I tell my friend that one of her friends is a backstabber?

I have been friends with this girl "Michelle" for about 10 years who has been friends with "Judy" for the same amount of time if not longer. I have recently found out that "Judy" has told "Sarah" who is a mutual friend of "Judy" and I, that "Michelle" has a job that she wouldn't want people knowing about. When "Judy" told "Sarah" about the job it was in a malicious way and talking **** about "Michelle". "Sarah" promised she wasn't going to say anything but told me anyway and I'm pissed off because "Judy" shouldn't be telling "Michelle's" business esp when she doesn't get along with "Sarah". Should I tell "Michelle" about the **** talking?