Hazy images produce negative influences on visual applications in the open air since they are in poor visibility with low contrast and whitening color. Numerous existing methods tend to derive a totally rough estimate of scene depth. Unlike previous work, we focus on the probability distribution of depth that is considered as a scene prior. Inspired by the denoising work of multiplicative noises, the inverse problem for hazy removal is recast as deriving the optimal difference between scene irradiance and the airlight from a constrained energy functional under Bayesian and variation theories. Logarithmic maximum a posteriori estimator and a mixed regularization term are introduced to formulate the energy functional framework where the regularization parameter is adaptively selected. The airlight, another unknown quantity, is inferred precisely under a geometric constraint and dark channel prior. With these two estimates, scene irradiance can be recovered. The experimental results on a series of hazy images reveal that, in comparison with several relevant and most state-of-the-art approaches, the proposed method outperforms in terms of vivid color and appropriate contrast.