We were a handful of plays and uncharacteristic drops from having a home NFC championship game after our 7-9 season. The Giants and the Ravens both backed into the playoffs the year they won it. Destiny is just a made up concept applied after the fact to whatever team manages to win a few games in a row at the end of the year. Every team in the playoffs has a shot some are just more likely than others.
I'd put the likelihoods in the following descending tiers.
A) Patriots
B) Cowboys, Falcons
C) Seahawks, Packers, Steelers, Chiefs
D) Giants
...
Z) Lions, Texans, Dolphins, Raiders