find probability of number in a matrix

Hi! I have a matrix

A=[2 1 4 0 0; 3 2 1 3 2; 0 2 0 2 1]

I want to find the probability of numbers 1,2,3,4 for every columns. When in the matrix there is a 0, if like there isn't nothing in its position.

for example: probability of 2 in the first column is 1/2; probability of 3 in the first column is 1/2; probability of 2 in the second column is 2/3 and so on

I want realize a matrix like this:

B = [1 0 1/3 1/2 0 1/2; 2 1/2 2/3 0 1/2 1/2; 3 1/2 0 0 1/2 0; 4 0 0 1/2 0 0]

first column indicates the values I want to find the probabilities and the other columns are the probabilities of this values in every column.

Thanks for help

Answer 1

[Alexandra Harkai]

You can sum all elements in each column that matches, and divide by the number of nonzero elements:

v = (1:4)'; % your numbers
B = cell2mat(arrayfun(@(x) sum(A==x,1)./sum(A~=0,1), v, 'UniformOutput', false)); % actual calc performed on each element of array v
B = [v, B]; % appending the first column of 1..4 numbers