One way to accomplish this is to use the contains function to get a logical array describing the locations of a specific string (in your example, 'GUUA'), and then summing this array to obtain the number of occurrences of this string. The number of occurrences can then be divided by the length of the cell array to obtain the probability:
c = {'GUUA','GUUA','UUAG','UUAG',...
'UAGC','UAGC','CGCC','CGCC'}; % Your cell array
p = sum(contains(c,'GUUA'))/length(c); % Probability
