So, in this season, the season 2015/2016, the English Premier League was won by Leicester.
The interesting thing is that in the season before, the season 2014/2015, Leicester ended the season in fourteenth place and if they had only 7 points fewer, would have been relegated to the second (Championship) league.
So, it is kind of a football/soccer miracle that they won the English Premier League.
I would like to know if there are any similar examples of football/soccer clubs that were at some season close to the relegation zone and then won the title in the next season?
Edit: I would like to note here that an examples from other leagues other than English Premier League are welcomed, and as I was requested to objectively define what it means to be "close to relegation zone", let us take for the purpose of the question only teams who were 7 or less points from the relegation zone in one season and then won the title in the next season.