Despite RNA-seq reads provide quality scores that represent the probability of calling a correct base, these values are not probabilistically integrated in most alignment algorithms. Based on the quality scores of the reads, we propose to calculate a lower bound of the probability of alignment of any fast alignment algorithm that generates SAM files. This bound is called Fast Bayesian Bound (FBB) and serves as a canonical reference to compare alignment results across different algorithms. This Bayesian Bound intends to provide additional support to the current state-of-the-art aligners, not to replace them.