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For example: An initial set $[1, 3, 4, 7, 2]$ sums to 17. By dividing each element by the sum, the elements sum to 1: $[1/17, 3/17,...2/17]$ sums to 1.

What is it called when a set of numbers are adjusted to sum to one?

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Perhaps you're thinking of a normalizing constant? In your example, the normalizing constant is $1/17$.

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In a statistics forum it is perhaps too obvious to underline that such numbers are often called probabilities, although such numbers aren't always probabilities.

In terms of English usage, proportion and fraction are also often used for such numbers. A fraction, however, can certainly exceed 1. 17/12 is such a fraction.

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