Abbott, who remained firmly opposed to equal marriage and who had recently banned his MPs to vote freely on the issue under penalty of dismissal from the party, who had subsequently suggested a plebiscite on the issue before backtracking since he was trying to prevent a vote on the equal marriage after the next federal election in 2017, was challenged by Malcolm Turnbull (picture 2) in the Liberal Party.
After getting enough support within the party, a vote could be held to choose the leader of the Liberal Party and that is Turnbull who won with a 44-54 vote!
By winning this victory, Turnbull becomes at the same time the new Australian Prime Minister (for information, there is no President in Australia, the Prime Minister is the President).
We don't know very well Turnbull's view on marriage equality yet, but he said that he could actually hold a plebiscite or also grant a free vote, adding that Australia was falling behind on the issue. We will probably have more details in the days or weeks ahead.