I stand corrected. I had been reading various things that stated 25%... without the 4 up and 1 back. Just came across this explanation:
"At the conclusion of the regular season, the 14 NHL teams not qualifying for the playoffs are entered in a weighted lottery to determine the initial draft picks in each round, seeded according to regular season standing. The 30th-place team has a 25% chance of winning the lottery, with odds diminishing to a 0.5% chance for the 17th-place team. A single selection from the lottery pool is made, with the winning team eligible to improve its draft order by up to four places, and no team eligible to drop more than one place. Only the 26th- through 30th-place teams, then, are eligible to receive the first draft pick. Consequently, the 30th-place team's chance of retaining the first overall pick (as opposed to winning the lottery outright) improves to 48.2%."