The maximum entropy method, or MAXENT, is variational approach for computing probability distributions given a list of moment, or expected value, constraints.
Here are some links for background info. A good overview of applications: http://cmm.cit.nih.gov/maxent/letsgo.html On the idea of maximum entropy in general: http://en.wikipedia.org/wiki/Principle_of_maximum_entropy
Use this package to compute discrete maximum entropy distributions over a list of values and list of constraints.
Here is a the example from Probability the Logic of Science http://books.google.com/books?id=tTN4HuUNXjgC&lpg=PA355&ots=H4NxnzJxT0&dq=probability%20the%20logic%20of%20science%2011.38&pg=PA354#v=onepage&q=probability%20the%20logic%20of%20science%2011.38&f=false
maxent ([1,2,3], [average 1.5]) Right [0.61, 0.26, 0.11]
The classic dice example
maxent ([1,2,3,4,5,6], [average 4.5]) Right [.05, .07, 0.11, 0.16, 0.23, 0.34]
One can use different constraints besides the average value there.
As for why you want to maximize the entropy to find the probability constraint, I will say this for now. In the case of the average constraint it is a kin to choosing a integer partition with the most interger compositions. I doubt that makes any sense, but I will try to explain more with a blog post soon.