Starting with 2015-2016, the NHL will use a triple-lottery to decide the draft order. Each team who does not qualify for the playoffs has a given lottery chance, if they are chosen, they pick first overall. After this, a second team is chosen, using the same probabilities, except that the team who won the previous lottery is not eligible; this second team will pick second overall. Finally, a third lottery is held, again with the same probabilities, only the first two teams are excluded, the winner picks third overall. The remaining teams pick in reverse standings order. It is reasonably straightforward with the aid of a modern desktop computer to compute the chance of obtaining a given pick after finishing in a particular spot and I have tabulated them thusly:
Darker blue shading indicates higher probabilities, and the displayed number is the percent chance of that particular outcome. Zero and one hundred are shown in solid white and blue. The basic lottery probabilities for the draws are shown in the first column of the table.
The last place team picks no lower than fourth, and is in fact most likely to do so than to pick in any other other particular spot.
If you prefer, you can compute the chance of picking in a particular spot or better by simply adding up the figures:
All seven of the lowest seven teams are more likely to fall at least one spot in the draft than to move up.