Assuming that only two candidates will actually get any electoral votes, the third place candidate is the candidate who receives the third-largest share of the popular vote in the general election. If three or more candidates actually do receive electoral votes, then the third place candidate is either the candidate with the third-most electoral votes (if there's of an Electoral College winner), or the candidate with the third-most votes from the House of Representatives state delegations (if the election goes to the House).

In the case of a tie for third place, I'll resolve equally to the tied candidates.