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.
[206.669, 249.705, 105.964, 40.305, 34.249, 17.207, 223.148, 25.656, 159.843, 166.678]