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.
[173.96, 73.119, 247.97, 93.716, 201.795, -9.589, 41.527, -52.06, 149.735, 36.604]