I think we are contending now, but I'm not sure the odds are in line with the spirit of the question. I think the most likely answer is next year.
We are team that is currently constituted to win 55 or so games, and will win a few less this year due to a lot of missed games by starters due to nagging but not degrading injuries. Next year, we would likely be a bit better just due to experience together and individual growth.
If we just draft a top pick, we can also expect a better bench. Brown, Zizic, Yabusele and a top rookie won't become stars next year, but they should improve on our current bench.
If we get a free agent like Hayward, or Griffin, I think we are a 60+ win team. We still might not be a favorite, but we will be considered clearly top 4.
If we cash in some future resources and also get another all-star caliber player, we have as good a chance as anybody.
I think the Cavs, the Warriors and the Spurs are awesome, but somewhat fragile teams. With just a bit of luck, I think they can be beaten.