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.
[99.596, -71.297, 227.526, 174.089, 113.776, 186.506, 245.166, 157.474, 79.164, -63.262]