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I think your denominator in your original equation is missing a second term. That is why you get a non-probability for your answer. See here: http://foxholeatheism.com/wp-content/uploads/2011/12/Bayes.jpg
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should be posted in Discussion, and not Main.
4. Open Threads should start on Monday, and end on Sunday.