Obtaining Values Within A Range

I've got a problem where I need to assign values to ranges between 0 and 3.

Eg.

RANGE VALUE
2-3 2.2
1-3 1.6
0-3 0.8
0-2 0.5
0-2 0.5
0-1 0.1
0-1 0.1
0-1 0.1
0-1 0.1

The values above are simply approximates done manually but I need it done automatically using a formula. The resulting values should be proportioned similarly to the ones above but they need to all sum up to 6 and be no more than 3 each.