normalizing reverse value of 0

I have the following problem

I have 3 options with different ranks:

A=3

B=0

C=0

I would like to normalize them to 0..1 scale.

The problem is that actually the value 0 is "better" than value 3, so I would reverse the values beforehand and use 1/A, 1/B and 1/C instead.

So the normalized weigh for A on the 0..1 scale would be:

(1/A)/((1/A)+(1/B)+(1/C))

For B:

(1/B)/((1/A)+(1/B)+(1/C))

For C:

(1/C)/((1/A)+(1/B)+(1/C))

However if A, B or C are zeros there can not be any reverse value. How to normalize in this case?

Thank you.