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, or if you've completed the How Little We Know quest you can convince them that you know the boss of the Omertas, and they will walk away.

Detailed walkthrough
The quest is pretty straightforward. While in the Legion's Fort, talk to Vulpes Inculta in Caesar's tent. He'll brief the player about an informant girl (Martina Groesbeck) who is either sided with the Legion or a friend of it, and is about to be hunted down by the Omertas. Travel to The Strip and walk through the two gates to get to Vault 21 casino/hotel, go then to the lower levels and follow the marker around; you'll eventually arrive at a room where three Omerta thugs are about to kill the woman. Now, there're various options available.

You can attack the thugs by surprise without saying a word, or talk to one of them. At this point, it's possible to convince them that Martina is working for the Legion, scaring them enough to leave without a fight, but only with a high enough speech skill (50 speech). If you don't have enough speech skill (or you just want to kill them), there's also a dialogue option that triggers a fight. One of the thugs carries a knife (and will attack in close combat), the others are equiped with a sawed off shotgun and a 9mm submachine gun. None of them wear any kind of armour (only suits) so it shouldn't be a difficult encounter. You can also use the speech option, and kill them quickly while they walk away. This will give you the challenge, the speech xp, and the kill xp plus loot. Noone except the thugs turn hostile if you kill them.

After you have dispatched them (either way), talk to the girl. She'll thank you and will answer a few questions about what she does at The Strip, stating she's working for the NCR, and assuring that she has nothing to do with the Legion. Once you're done talking, return to the Fort in order to collect your XP reward. Vulpes will explain that Martina actually works for a Legion's frumentarii infiltrated within the ranks of the NCR, and inmediately begin the quest I Put a Spell on You on the Legion side.