Since the 1099-S was split into thirds, do the same for the basis (purchase price) of the home. 

Is the purchase price a value that follows how the sold price was split? or is the purchase price an interchangeable value?

I assumed (perhaps incorrectly) that it was split evenly. If you only owned 1/3, you only purchased 1/3, but if the ratio is something different, use the accurate percentage.
When you enter the purchase price, enter the price for only your section. I hope that makes sense.

So is the purchase price based on ownership percentage?

i.e:
Split during purchase: 33/33/33
Split during sale: 70/30/0

Would the first person report the purchase price at 33% or 70%?

33% because that was their basis. I don't understand why it went from 33 to 70 (or zero). Is there more to the story? Did someone buy someone out?

No the owner released their share of the property and allowed one of the member to absorb their share