One hurdle newcomers have to applied Bayesian work is understand the notation. Coming from a mathematical background, one might think that p(x) is the same function as p(y) just evaluated at x and y, respectively. Instead in Bayesian notation, these typically refer to the marginal density (or mass) function for x and y, respectively. Similarly p(x|y) is not the same function as p(y|x), but instead the first is the function describing the conditional density (or mass) function of x given y and the second is the conditional density (or mass) function of y given x. Attempts to rectify this notation seem to make the notation overly complicated and therefore, the differences are made implicit. For more discussion of this, please see this post.