Python function for Probability - needs numeric integration

I need a python function for the following:

I have lists of predicted values for X, IE: [X1, X2 ....Xn].
Each X is expressed as a mean and a variance and has normal distribution.
So the list looks like [(5, 1), (9, 3), (7, 4).....]
The list can have any length

The function should return a corresponding list giving the probability that each X will be less than all the other Xs simultaneously.
All the values in the returned list should sum to 1.
For example in the simplest case were my list was [(3,1), (3,1), (3,1)] the function should return [0.33, 0.33, 0.33]

The mathematical solution to this problem is described here:
https://stats.stackexchange.com/questions/44139/what-is-px-1x-2-x-1x-3-x-1x-n?lq=1

Please only apply if you are certain that you understand the maths correctly.