This problematic situation should be resolved by using the 4 Ds of a difficult conversation (Define, Defuse, Discuss, and Decide).
First, we would need to "define" the problem. At this stage, Jessie would have to explain the situation to the mediator, explain why he suspected Steve, and tell all the details about the confrontation. In the stage known as "defuse," we would have to try to calm both participants down. This would most likely be done through calm conversations and the use of reason. After, we would enter the stage of "discuss." This stage would require us to talk things over, confront the problem, and brainstorm ideas. Finally, in the stage known as "decide" we would need to definitely establish what happened and what actions we can take to solve the problem.