How leaders are chosen in parliamentary democracies

Premier Terry Mills of Australia's Northern Territory went to Japan for an official visit a few days ago.  While there he got a phone call. They told him the parliamentary caucus of his Country Liberal party had met and voted 11-5 to replace him with his cabinet colleague, Adam Giles. Mr Mills accepted the decision by phone and is returning as a backbencher. He will support the Giles government, he says. Premier Giles becomes the first aboriginal chief minister in Australia.

Remind me again: why is Justin Trudeau spending six months and a million dollars to buy the leadership of the Liberal Party with the votes of people who won't even be party members after he succeeds?

(Wish I had prizes for the answer to this one!)