The Finger of Suspicion

 is a quest in Fallout: New Vegas.

Talk to Vulpes in Caesar's tent, and he will give you the quest. Travel to Vault 21 at the strip and kill 3 Omerta Thugs. Talk to the girl they were trying to kill. Return to Vulpes.

Note: The quest can be completed without killing the thugs, if you have a high enough speech skill you can convince the thugs that the girl is with the legion and they will walk away.

Detailed walkthrough
Go to the Fort and talk to Vulpes Inculta in Caesar's tent, he should talk about a girl (Name needed) that is either sided with the legion or a friend of his. Fast travel to the strip (If you can) and walk through the two gates to get to Vault 21 casino/hotel, go to the lower levels and follow the marker around, you should get to a room with three omerta thug one of them should speak to you and at this point you can choose to convince them that she is with the legion, thus making them leave, but only with a high enough speech skill.

You can also choose to kill them but that option has been untested so far.

After you have done either talk to the girl and she should thank you, you can ask her a few questions about the NCR etc. and she says that she has nothing to do with the legion.

Once you have talked with the girl return to Vulpes and you will be rewarded with XP. You should then be able to begin the quest I Put a Spell on You on the legion side.