So I've found some examples where "the share of" has a similar meaning to "the percentage of".
1.The fracking boom and a more modest clean-energy boom have increased this country’s share of energy production and held down costs worldwide. (source)
2. His share of the vote rose by 15 percentage points among Hispanics. (source)
3. Engel's law' states that as income increases, the share of expenditure on food in total household expenditure tends to decrease. (source)
4. Since 2000, the proportion of the prison population made up of whites and blacks had declined slightly; the share of Hispanics increased. (source)
What do these examples have in common? According to many dictionaries, share is a part of something that has been divided between several people or things. I think this meaning is only related to the 2nd and 3rd examples. In the 1st and 4th examples, I don't think energy production or prison population is shared between anybody or anything.
So, what kinds of nouns can go with "the share of" and create phrases which have a similar meaning to "the percentage of something"?
P.S. I would love it if your answer includes an explanation regarding specifically to example 4. That's the most confusing one out of all. Thank you!