Our chances of winning the 2nd pick depends on who wins the first pick, and then our chances of winning the 3rd pick depend on who wins the second (and first) pick. Obviously, all teams benefit from teams with better odds (Toronto, Edmonton, etc...) winning the first two picks as this increases the odds the most for us (and everyone else) of winning the lottery at all. Let's look at two scenarios:
The Devils have at best a 3% of winning the first pick.
Let's say Toronto and Edmonton (the two bottom teams) win the first two picks:
If Toronto wins the first pick the Devils increase to a 3.75% chance of winning the second pick. This is our best chance of winning the second pick, if we don't win the first. Then, if Edmonton wins the second pick, the Devils chances of winning the 3rd pick increase to 4.51%. However, with that order, the chances that we would have won the lottery BY the 3rd pick are 10.85%, which happens to be our best chance of winning the lottery in any of the three rounds.
Now, let's look at another scenario, when the bottom two teams don't win the first two picks:
Let's say the Sabres (8th pick as of now) win the first pick. Then the Devils chances of winning the second pick increase to only 3.19%. If the Canucks (3rd pick as of now) then win the 2nd pick in the lottery, the Devils chances of winning the 3rd pick increase to 3.64%. In this scenario, the chances that we would have won the lottery by the 3rd pick are 9.51%.
This is a decrease of 1.34% from the first scenario. Either way, we have to get pretty lucky to win the lottery, but as you can see, it's not improbable at all.