We derive a closed-form expression for the exact pairwise error probability (PEP) of a non-uniform memoryless binary source transmitted over a Rayleigh fading channel using space-time orthogonal block codes and maximum a posteriori (MAP) detection. The expression is easy to evaluate and holds for any signaling scheme. We then use this result to minimize the bit error rate of the binary antipodal signaling scheme. Numerical results for the case of binary antipodal signaling (BPSK and optimal) verify the accuracy of our formula and quantify substantial gains of MAP decoding over maximum likelihood (ML) decoding for sources with strong non-uniformity.