With the increasing demand for robust person Re-ID in unconstrained environments, learning from datasets with noisy labels and sparse per-identity samples remains a critical challenge. Existing noise-robust person Re-ID methods primarily rely on loss-correction or sample-selection strategies using softmax outputs. However, these methods suffer from two key limitations: 1) Softmax exhibits translation invariance, leading to over-confident and unreliable predictions on corrupted labels. 2) Conventional sample selection based on small-loss criteria often discards valuable hard positives that are crucial for learning discriminative features. To overcome these issues, we propose the CAlibration-to-REfinement (CARE) method, a two-stage framework that seeks certainty through probabilistic evidence propagation from calibration to refinement. In the calibration stage, we propose the probabilistic evidence calibration (PEC) that dismantles softmax translation invariance by injecting adaptive learnable parameters into the similarity function, and employs an evidential calibration loss to mitigate overconfidence on mislabeled samples. In the refinement stage, we design the evidence propagation refinement (EPR) that can more accurately distinguish between clean and noisy samples. Specifically, the EPR contains two steps: Firstly, the composite angular margin (CAM) metric is proposed to precisely distinguish clean but hard-to-learn positive samples from mislabeled ones in a hyperspherical space; Secondly, the certainty-oriented sphere weighting (COSW) is developed to dynamically allocate the importance of samples according to CAM, ensuring clean instances drive model updates. Extensive experimental results on Market1501, DukeMTMC-ReID, and CUHK03 datasets under both random and patterned noises show that CARE achieves competitive performance.