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.
[191.763, -81.332, 131.218, 227.675, 246.322, 179.752, 14.497, 241.311, 249.791, 65.909]