Please forgive my lack of knowledge - it's been a while since I've taken classes in statistics, and even then, it was not my strong point. I'm trying to recall a method used to upweight all values in the distribution using a uniform distribution - it was called something like k+1? Essentially, the method consisted of adding a specific value to all elements in the distribution, to emulate the effect of sampling with a uniform distribution for all elements, so that no element has a value of 0 or close to it.
Edit: I recently (it's currently October 2015) came across the term for this method: it's called adding pseudocounts (or Laplace estimators), at least in the context that I was referring to it. Just adding this in case anyone else can use that information.