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.
[36.099, 129.951, -22.335, 127.189, 139.229, 17.204, -3.077, -14.713, 154.746, 186.923]