In Python, how can I distribute a set of numbers randomly onto a grid/matrix?

I have the following problem: I want to generate a 100x100 grid (numpy.ndarray) by filling it with numbers, out from a given list ([-1,0,1,2]). I want to distribute them randomly on this grid. Also, the numbers must maintain the following ratios: the number 0 must occupy 10% of the grid, while the remaining numbers have a 30% ratio each, so their sum equals 100%. Using np.random.choice() I was able to generate random numbers, each distributed with the associated probabilities. However, I run into problems because I have to make sure that the number 0 makes exactly 10% of the entire grid, and the non-zero numbers exactly 30% each. Using the np.random.choice() function, this is not always the case (especially if the sample size is small), because I have only assigned probabilities, and not ratios:

import numpy as np

numbers = np.random.choice([-1,0,1,2],(100,100),p=[0.3,0.1,0.3,0.3])
print(np.count_nonzero(numbers)) #must be = 0.1 always!

Another idea I had was to initially set the entire matrix as np.zeros((100,100)) and then fill up only 90% of it with non-zero elements, however, I don't how to approach this problem such that the numbers are distributed randomly on the grid, i.e., random location/index.