I currently am dealing with a coworker with that particular attitude....kinda like "You're beneath me" stank aura. Honestly, I just ignore her until she either speaks to me or that orders from above tells me that I need her to help me on an assignment. I NEVER make small talk with her. I don't even say hi/good bye to her. I'm not limited to speaking to her to be rude or passive aggressive, but I understood long ago that she just doesn't like to interact with certain people for whatever reason. Tried several times and methods to extend the olive branch, but I was rejected. I don't try to question it or challenge her anymore. Her feelings are her own and I've accepted that. She seems to understand that when I speak to her these days, it is always business.
Trying keeping everything with that person with a distant attitude. Don't even bother with the idle pleasantries and or office banter. Keep your conversations professional, short, and simple, and end interaction quickly. If you're naturally a friendly person, it does feel weird at first to be so blunt, but it'll gets easier over time.