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.
[208.486, 177.568, 244.384, 217.595, 28.686, 216.641, 86.543, -71.308, 142.539, 206.143]