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.
[174.824, 156.297, 161.416, 156.954, 94.712, 36.892, 1.437, 137.084, 117.004, 224.81]