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.
[-43.693, 86.666, 188.625, -70.65, 128.014, -14.168, 200.964, 78.371, -27.925, 192.358]