In this task, you will be given a list of numbers. The goal is to divide all the numbers in the list by a constant such that the sum of the resulting list is 1. The output should be rounded to 3 decimals.
[237.751, 48.207, 22.029, 149.61, 243.367, -38.305, -77.657, -32.622, 84.283, 22.583]