Diffusion magnetic resonance imaging (MRI) is a neuroimaging technique for probing the anatomical structure of tissues through quantification of the water diffusion process. Using diffusion MRI to reconstruct white matter fiber tracts and assess tissue connectivity, also known as fiber tracking, is arguably the most important applications of diffusion MRI. Although a number of innovative and compelling techniques are available for fiber tracking, only a few provide an elegant evaluation of the statistical (spatial) uncertainties. In this paper, we propose spatial modeling of positive definite diffusion tensor matrices via a directed acyclic graph auto-regressive model and develop an efficient probabilistic fiber tracking algorithm. We illustrate our proposed method via numerical studies and application to a real dataset.