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Bayesian conclusion scale with uneven data distribution. Possible?

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I have two sets of data distribution between 0 to 100%. I was thinking of using the Bayes theorem of explaining the data distribution. More info on Bayes theorem:
http://en.wikipedia.org/wiki/Bayes%27_theorem

However, both of my data is not normally distributed.

1st dataset: 0-100% with midpoint of 16.66%. (Highest value obtained is 85% while lowest value 0%)

2nd dataset: 0-100% with midpoint of 16.66%. (Highest value 35% with lowest value 0%)

Both scales/data are independent of each other. However, I'm not sure which kind of probability theory to use. I was thinking Bayesian, but I'm not sure if Bayesian theory works with uneven data distribution. Can anyone tell me which theory should I be looking at? Can Bayesian work for uneven data distribution?

Thank you

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