The new Prime Minister is set to be elected during the next week or so. The leading candidates are Sanna Marin, Minister for Transportation, and Antti Lindtman, chairman of the SDP parliamentary group. Rinne still wants to continue as SDP chairman, though. Were Marin elected, she would be the country's third female PM and we would also be in a situation where all government coalition parties are led by women.
SDP's party council has elected Sanna Marin to be their candidate for new Prime Minister by the tightest of margins, 32 votes for Marin, 29 for Lindtman. In advance it was speculated that the "red-green" types would support Marin, while the labour union types would gravitate toward Lindtman -- Rinne though has a union background but still backed Marin.
Marin will officially become PM in a few days when the parliament elects her for the office; the coalition parties have already agreed. At 34, she will become the youngest female Prime Minister in the world, certainly at the moment (she's younger than Jacinda Ardern), maybe ever?