It has been shown that human combination of crossmodal information is highly consistent with an optimal Bayesian model performing causal inference. These findings have shed light on the computational principles governing crossmodal integration/segregation. Intuitively, in a Bayesian framework priors represent a priori information about the environment, i.e., information available prior to encountering the given stimuli, and are thus not dependent on the current stimuli. While this interpretation is considered as a defining characteristic of Bayesian computation by many, the Bayes rule per se does not require that priors remain constant despite significant changes in the stimulus, and therefore, the demonstration of Bayes-optimality of a task does not imply the invariance of priors to varying likelihoods. This issue has not been addressed before, but here we empirically investigated the independence of the priors from the likelihoods by strongly manipulating the presumed likelihoods (by using two drastically different sets of stimuli) and examining whether the estimated priors change or remain the same. The results suggest that the estimated prior probabilities are indeed independent of the immediate input and hence, likelihood.