In legal practice, judges apply the trichotomous dogmatics of criminal law, sequentially assessing the elements of the offense, unlawfulness, and culpability to determine whether an individual's conduct constitutes a crime. Although current legal large language models (LLMs) show promising accuracy in judgment prediction, they lack trichotomous reasoning capabilities due to the absence of an appropriate benchmark dataset, preventing them from predicting innocent outcomes. As a result, every input is automatically assigned a charge, limiting their practical utility in legal contexts. To bridge this gap, we introduce LJPIV, the first benchmark dataset for Legal Judgment Prediction with Innocent Verdicts. Adhering to the trichotomous dogmatics, we extend three widely-used legal datasets through LLM-based augmentation and manual verification. Our experiments with state-of-the-art legal LLMs and novel strategies that integrate trichotomous reasoning into zero-shot prompting and fine-tuning reveal: (1) current legal LLMs have significant room for improvement, with even the best models achieving an F1 score of less than 0.3 on LJPIV; and (2) our strategies notably enhance both in-domain and cross-domain judgment prediction accuracy, especially for cases resulting in an innocent verdict.