Probation is a crucial institution in modern criminal law, embodying the principles of fairness and justice while contributing to the harmonious development of society. Despite its importance, the current Intelligent Judicial Assistant System (IJAS) lacks dedicated methods for probation prediction, and research on the underlying factors influencing probation eligibility remains limited. In addition, probation eligibility requires a comprehensive analysis of both criminal circumstances and remorse. Much of the existing research in IJAS relies primarily on data-driven methodologies, which often overlooks the legal logic underpinning judicial decision-making. To address this gap, we propose a novel approach that integrates legal logic into deep learning models for probation prediction, implemented in three distinct stages. First, we construct a specialized probation dataset that includes fact descriptions and probation legal elements (PLEs). Second, we design a distinct probation prediction model named the Multi-Task Dual-Theory Probation Prediction Model (MT-DT), which is grounded in the legal logic of probation and the Dual-Track Theory of Punishment. Finally, our experiments on the probation dataset demonstrate that the MT-DT model outperforms baseline models, and an analysis of the underlying legal logic further validates the effectiveness of the proposed approach.