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.
[197.283, 68.063, -23.564, 105.345, -53.72, -14.883, 185.644, 174.521, 66.365, 151.724]