I inadvertently left my wedding ring at a restaurant and suspect the waiter lifted it. I filed a police report and put an ad in the paper, offering a reward. Am I obligated to pay the reward?
Unless you can prove that the waittress stole your ring, then you'd have to pay the reward. Your assumptions, presumptions, feelings, suspicions, etc. wouldn't hold any water.
An offer of reward is like any other offer to the general public; like a store coupon, or "sale" offer. That is, if a person sees your offer, or has Notice of your offer (promise of a reward), and the person complies with your offer (returns your ring to you), then a contract has been made, and compliance will be your responsibility.