This would make a 3-way draw equivalent to 2nd place, which I think is wrong.
To codify the linear order described by yebellz statement in numeric terms, we could use an expression along the lines of
(players below you) + 1/(players above you + 2)
But that’s needlessly messy. This ordering would follow automatically if we had some prize pool like we discussed above (a prize pool would also make clearer how to compare different situations with probabilities assigned to outcomes). I think all that’s necessary for the prize pool to induce the “correct” preference of rankings is that it is strictly increasing between each placement. (Edit: No, I was wrong. See reply by @martin3141 in the other thread)