This article describes a probabilistic formulation of a Weighted Power minimization Distortionless response convolutional beamformer (WPD). The WPD unifies a weighted prediction error based dereverberation method (WPE) and a minimum power distortionless response beamformer (MPDR) into a single convolutional beamformer, and achieves simultaneous dereverberation and denoising in an optimal way. However, the optimization criterion is obtained simply by combining existing criteria without any clear theoretical justification. This article presents a generative model and a probabilistic formulation of a WPD, and derives an optimization algorithm based on a maximum likelihood estimation. We also describe a method for estimating the steering vector of the desired signal by utilizing WPE within the WPD framework to provide an effective and efficient beamformer for denoising and dereverberation.