Earlier attempts to show that simpler theories always have higher prior probabilities have failed, but there is a restricted circumstance in which the claim is right.
Current organisms have a higher probability of sharing a single code if the common ancestry hypothesis is true than they'd have if the hypothesis of separate ancestry were true. That is, the simpler hypothesis has the higher likelihood in the technical sense of "likelihood" used in statistics.
One influential philosophical position about the use of probability in science holds that probabilities are objective only if they are based on micro-physics; all other probabilities should be interpreted subjectively, as merely revealing our ignorance about physical details. I have argued against this position, contending that the objectivity of micro-physical probabilities entails the objectivity of macro-probabilities.
I think that the existence of Beethoven is remarkable, but I do not bristle at the suggestion that this event had a low probability given the initial state of the universe.
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