In supervised classification, probabilistic classifiers output a probability distribution over classes. However, these probabilistic estimates often lack reliability, which is crucial for effective decision-making. This paper introduces a nearest neighbor-based recalibration method designed to improve the reliability of probabilistic classifiers in multiclass problems. Our proposed approach corrects prediction biases by using local information via multivariate-response k nearest neighbor regression. Experimental evaluations on several renowned benchmark datasets using different classifiers confirm the effectiveness of our method relative to other recalibration approaches. The results highlight the proposed method's capability to provide more accurate and reliable class probability estimates.