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.
[14.054, 170.398, -93.473, -59.652, -71.84, 131.006, -93.699, 231.026, -20.538, 110.174]