This study investigates psychological factors influencing belief in AI predictions about personal behavior, comparing it to belief in astrology and personality-based predictions. Through an experiment with 238 participants, we examined how cognitive style, paranormal beliefs, AI attitudes, personality traits, and other factors affect perceived validity, reliability, usefulness, and personalization of predictions from different sources. Our findings reveal that belief in AI predictions is positively correlated with belief in predictions based on astrology and personality psychology. Notably, paranormal beliefs and positive AI attitudes significantly increased perceived validity, reliability, usefulness, and personalization of AI predictions. Conscientiousness was negatively correlated with belief in predictions across all sources, and interest in the prediction topic increased believability across predictions. Surprisingly, cognitive style did not significantly influence belief in predictions. These results highlight the "rational superstition" phenomenon in AI, where belief is driven more by mental heuristics and intuition than critical evaluation. We discuss implications for designing AI systems and communication strategies that foster appropriate trust and skepticism. This research contributes to our understanding of the psychology of human-AI interaction and offers insights for the design and deployment of AI systems.