There's now only 10 games left in the season and it seems all but assured that the Kings will end up keeping their draft pick, which needs to be in the top-10 to avoid it going to Chicago. At 26-46, the Kings are currently sitting with the 6th worst record in the NBA (and only like 3 games out of the 8th spot in the Eastern Conference, but hey, whatever).
The two closest teams to Sacramento in the standings are the Detroit Pistons (28-44) and Denver Nuggets (28-45). Between these three teams, these final 10 games will likely decide the lottery order from 6-8, which seems to be the slot the Kings will inevitably fill. The difference between 6th and 8th in the lottery is fairly significant in terms of chances of getting a top-3 pick, but that's before the little known "Kings can't jump up in the lottery" clause in the CBA is activated*.
Schedule wise, the Pistons have the easiest remaining schedule simply by virtue of being in the Eastern Conference. 7 of their final 10 games are against teams with below .500 records. The Kings have the next easiest schedule with 6 games left against teams with below .500 records, while Denver has just 3, including one against the Kings on April 12th in what will be George Karl's return to Denver.
It will be interesting to see where the Kings land in the lottery, especially in a draft so full of promising young big men. If I had to guess I can see the Kings overtaking Denver in the standings, although Sacramento might take the opportunity to rest guys like DeMarcus Cousins and Rudy Gay as the season begins to wind down in order to avoid injuries.
*not an actual clause, but it might as well be