I was actually doing some research on this the other day.

The last lockout,

"Teams that failed to qualify for the Stanley Cup Playoffs in the three seasons before the Draft, or were not awarded the first overall selection in the previous four NHL Drafts had the best chance of winning the lottery by being awarded 3 balls. If a team met one of the criteria above, they were awarded 2 balls, and if a team met more than one of the criteria, they were awarded only 1 ball."

In this lockout, that would mean:

Calgary, Columbus, Toronto, Dallas, Winnipeg, Carolina, Minnesota would all have 3 balls and a 6% chance at 1st overall.

The teams with 2 balls would be Colorado, St. Louis, Islanders, Tampa, Florida, and Anaheim which would give them a 4% chance at 1st overall.

The other 17 teams would have 1 ball and a 2% chance at 1st overall. Also, Columbus holds LA's 1st (Carter/Johnson trade) which would boost their chances to 8% and the best team to land the #1 pick.

Assuming the NHL uses the same criteria, expect something like this.