This question was inspired by a Stack Overflow question forwarded to me by Matt Simoneau.
Given a vector x, make an indexed probability vector p that shows the likelihood of each unique element of x occurring. You can assume that x will always be composed of integers greater than 0.
For example, if x is [4 4 4 4] then the number 4 is 100% likely to occur and no other number has any likelihood of occurring. By convention, p has as many elements as the highest number in x. This makes the indexing straightforward. So in this case, p = [0 0 0 1]. That is, p(4) = 1, which is to say that 4 occurs with 100% probability, as noted above. Note that p has no dependence on the order of the elements in x.
If
x = [1 2 1 2 1 2 1 2 1 2]
then
p = [0.5 0.5].
And if
x = [5 5 2 8]
then
p = [0 0.25 0 0 0.5 0 0 0.25]
Solve

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