Lottery Confusion: 25% or 48.2%?

What chance do the Islanders have of picking first overall in the 2009 Draft if they finish in 30th place? Is it 48.2%? Or is it 25%? Both numbers have been circulating, causing understandable confusion. I think I have the explanation. If not, then I've probably launched an explosion of misinformation for which I will pay dearly.

In any case, as I understand it, the Islanders have a 25% chance of actually winning the lottery. That is, being the team that is selected in the random drawing, automatically giving them the No. 1 pick. However, their chances of picking first overall rise to 48.2% due to the fact that teams 6-14 could win the lottery without displacing the Islanders in the No. 1 slot. Those teams can only move up four places if they are selected, so, in a sense, if one of those teams wins, the Isles win as well.

This is all illustrated here, which I was reminded of by the post here.