It seems that when the host disconnects the player who was second in joining the table becomes the new host. This even led to the awkward situation that I became host as a spectator, because I had joined the table before the second player.
It would be good, if the host remains the same after reconnecting to the game. You could for example check at the end of the game, whether the host from the beginning of the game is still present.
And if the host is not present, it is probably preferrable to make the other actual player(s) the new host before picking a spectator.