Anti-sparse coding aims at spreading the information uniformly over representation coefficients and can be naturally expressed through an ℓ∞-norm regularization. This paper derives a probabilistic formulation of such a problem. A new probability distribution is introduced. This so-called democratic distribution is then used as a prior to promote anti-sparsity in a linear Gaussian inverse problem. A Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of interest. To scale to higher dimension, a proximal Markov chain Monte Carlo algorithm is proposed as an alternative to Gibbs sampling. Simulations on synthetic data illustrate the performance of the proposed method for anti-sparse coding on a complete dictionary. Results are compared with the recent deterministic variational FITRA algorithm.