Applying for Internships with Possession of Marijuana Charge

I am currently a Junior persuing a degree in finance. I also am currently applying to different investment banks for a summer internship. About 3 years ago when I was a freshman I got caught with a little bit of marijuana and was charged with possession of marijuana. I went through a pretrial diversion program which ended up with my charges being dropped. I do not smoke marijuana anymore but an still very worried about this charge. My question is that I know most investment banks do fingerprinting back ground checks. I believe this charge will show up once they do a background check even if I didn't get convicted, how bad will this effect my chances of getting/maintaining an internship over the summer? The internship will be in a different state that then where I was charged.