How does TFT choose who fights and when you die?

I've been late in the game several times now and seen some really stupid things.

My last game there were 3 of us left and the game pitted me against the same guy 6 times in a row while the third guy watched without losing any health. Then when I beat the other guy I had 3 health left and the 64 health guy sitting on the side only needed one round to beat me after losing 3 matches in a row to me???

I've also 'lost' when I had 30-40 health left in the round all in one go, while in another game I spectated after losing and watched two guys fight 6 more rounds between the two of them only losing small amounts of health each round. This is completely inconsistent and makes no sense at all.

Can anyone explain how the game is choosing who fights who and why sometimes it just decides to boot you outright while in other instances it lets people slowly whittle each other down? All of these instances have been post dragon fight so its not like they're in radically different segments of the game.