Image geo-localization aims to determine the geographic location of a query image. While Multimodal Large Language Models (MLLMs) show potential for this task due to their rich world knowledge and explainable abilities, they often struggle with confirmation bias, i.e., committing to early, potentially incorrect guesses caused by visual clues with varied geographic likelihoods. In this paper, we propose GeoBayes, a novel training-free framework that formulates geolocalization as a Maximum a Posteriori (MAP) estimation task over multiple geographic hypotheses and performs probabilistic thought via sequential Bayesian reasoning. GeoBayes treats each visual object and its associated geographic clues as probabilistic evidence, integrating them iteratively through a Hypothesize–Verify–Update loop. At each step, it evaluates how new evidence supports existing hypotheses and updates their posterior probabilities, gradually converging on the most probable location. This allows GeoBayes to explicitly quantify and fuse the varied geographic probabilities implied by various visual elements, reducing the risk of overcommitting to misleading clues. Furthermore, considering the natural hierarchy of geographic labels (e.g., country, city), GeoBayes introduces a state memory mechanism that stores hypotheses, inference context, and evidence scores across levels. This design enables the framework to propagate prior knowledge across levels of the geographic hierarchy and incorporate geographic structural constraints into the Bayesian update process, achieving a coarse-to-fine geo-localization. Experiments on IM2GPS3k and YFCC4K show that GeoBayes improves MLLM-based geo-localization accuracy without extra training. This demonstrates the effectiveness of probabilistic reasoning for robust and interpretable geo-localization.