Firstly, I think NS is right in that the only way Labour could win 2020 would be for the Tories to lose it. In fact the political wisdom states that parties rarely win elections but only do so by being the least worse one going. That said, the state of the political milieu these days could mean 2020 is up for grabs.
Yvette Cooper sounds as vacuous and as plastic as Ed Miliband. Andy Burnham comes a cross as the usual political animal and sounds like a safe dull bet. Liz Kendall is the keen puppy dog who is making bold moves but could fizzle out and sounds too much like a Tory. All three are just trying to adjust their sails to suit what they see as where the wind is blowing but have no personal convictions and ideas of their own, and are in effect trying to 'buy' their way into No. 10.
The only one coming across as 'real' is Jeremy Corbyn and with the likes of austerity and the Greek type anger at this he may be the one who could attract a good portion of the people to him. Sadly it is mainly the Party and party machine that will decide and they tend to be more in the other threes' bubble. If he does manage to win it then we could see meltdown within the Labour party but with the people behind him and the party.