Real-time systems tend to be probabilistic in nature because of the performance variations of complex chips. We present an execution allowance based fixed priority scheduling scheme for probabilistic real-time systems. This scheme consists of a probabilistic Worst Case Execution Time reshaping algorithm and a fixed priority scheduling strategy. It assigns a specific execution allowance to each task and schedules tasks under the Rate Monotonic policy. We present a schedulability analysis and show how to determine an appropriate execution allowance for each task. Evaluation shows that our proposed scheme can significantly outperform the existing approaches.