Transductive inference has been widely investigated in few-shot image classification, but completely overlooked in the recent, fast growing literature on adapting vision-langage models like CLIP. This paper addresses the transductive zero-shot and few-shot CLIP classification challenge, in which inference is performed jointly across a mini-batch of unlabeled query samples, rather than treating each instance independently. We initially construct informative vision-text probability features, leading to a classification problem on the unit simplex set. Inspired by Expectation-Maximization (EM), our optimization-based classification objective models the data probability distribution for each class using a Dirichlet law. The minimization problem is then tackled with a novel block Majorization-Minimization algorithm, which simultaneously estimates the distribution parameters and class assignments. Extensive numerical experiments on 11 datasets underscore the benefits and efficacy of our batch inference approach. On zero-shot tasks with test batches of 75 samples, our approach yields near 20% improvement in ImageNet accuracy over CLIP's zero-shot performance. Additionally, we outperform state-of-the-art methods in the few-shot setting. The code is available at: https://github.com/SegoleneMartin/transductive-CLIP.