Traditional travel choice models rely on large-scale structured data and often struggle to balance behavioral interpretability with predictive accuracy. Large Language Models (LLMs) offer a promising alternative for human-like cognitive decision-making. However, general LLMs often suffer from behavioral misalignment during direct inference due to a lack of domain-specific priors. To address this, this paper proposes ReCAP, a prediction framework integrating retrieval augmentation with behavioral preference calibration. The framework follows a Retrieve-Induce-Deduce paradigm involving three stages. First, a balanced retrieval strategy based on semantic vector space matches homogeneous reference groups. This approach effectively mitigates sample class imbalance and long-tail distribution biases found in traditional retrieval. Second, the framework utilizes the few-shot capabilities of LLMs to distill structured behavioral preference profiles covering sensitivities to time, cost, and comfort. These profiles serve as explicit prior constraints to dynamically calibrate the general model into a domain expert.  Finally, the model makes context-specific predictions based on these profiles. Experiments on the Swissmetro dataset demonstrate that ReCAP excels in both micro-level individual choice classification and macro-level mode share fitting. Compared to baselines like multinomial logit (MNL) and random forest (RF), it improves accuracy and the weighted F1 score by over 10% on average. Furthermore, it significantly reduces the Jensen-Shannon divergence (JSD) between predicted and true distributions, alleviating identification bias against non-dominant categories. Additionally, the generated natural language reasoning chains elucidate the trade-offs behind decisions, enhancing the interpretability and transparency of behavioral predictions.