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.
[179.573, -62.25, -20.48, 92.487, 146.211, 148.329, 56.409, -65.715, 119.242, 219.678]