We present a novel routing approach for multichannel cognitive radio networks (CRNs). Our approach is based on probabilistically estimating the available capacity of every channel over every CR-to-CR link, while taking into account primary radio (PR). Our routing design consists of two main phases. In the first phase, the source node attempts to compute the most probable path (MPP) to the destination (including the channel assignment along that path) whose bandwidth has the highest probability of satisfying a required demand D. In the second phase, we verify whether the capacity of the MPP is indeed sufficient to meet the demand at confidence level delta. If that is not the case, we judiciously add channels to the links of the MPP such that the augmented MPP satisfies the demand D at the confidence level delta. We show through simulations that our protocol always finds the best path to the destination, achieving in some cases up to 200% improvement in connection acceptance rate compared to the traditional Dijkstra.