This is based entirely on section214's yeoman work assessing the State of the 2007-08 Season. We'll keep tabs, watching scoreboards and judging moods.
Here, in chart form, is a breakdown of 214's consideration on the probabilities the Kings make the postseason. (We'll assume the West's top five teams -- Phoenix, New Orleans, Dallas, San Antonio and Los Angeles -- won't implode to lottery levels.) And remember, the Kings need to achieve its objective (finishing 25-11) while seeing three other teams meet their doom by finished with the 'required' record or worse.
Sacramento 22-24 25-11 Ask later
Houston 27-20 20-15 Plausible
Portland 27-19 20-16 Plausible
Denver 28-18 19-17 Unlikely
Golden State 29-19 18-16 Maim Baron!
Utah 30-18 17-17 No f'n way
Clearly, the biggest obstacle is finishing 25-11. The second biggest obstacle: Watching Denver, Golden State or Utah falter while Portland and Houston refuse to go on hot streaks.
This is rather bleak, even by 'improbable playoff run' standards.