I guess we should be rooting for no teams outside of the top 3 to jump into the top 3. If we get jumped we want to get jumped by the #2 or #3 team so our odds increase significantly for the #2 or #3.
I don't think that's correct.
If no one outside the top 3 jumps in, then (before the reveal of the top 3) we know that the Suns (250 chances) had to beat out only Memphis (199 chances) and Dallas (156). It also means that their chance of having fallen to #4 is zero.
If a low-odds team jumps in,
a) Now we have to sweat the Suns falling to #4, and
b) Before the reveal, it's (roughly) equally likely that the team that jumped did so by snagging the #1, #2, or #3 pick. It's a 33% chance they snagged #1, which would immediately take the Suns out of the running for that. If #4 is revealed and it's not Phoenix, it's true that the Suns are now relatively more likely to have won the #2 pick than if they had been up against the other big hitters, but only at the expense of having lost the chance at #1.
This could all be made rigorous, but it's more work than I can take on now. However...
* It is possible to calculate the Suns' exact odds of having won each pick
if we get everything through #4 revealed and no one has jumped up. In that case we know that the three winners were PHO/MEM/DAL, with these possible scenarios:
1. PHO, 2. MEM, 3. DAL
(250/1000)*(199/750)*(156/551) = 0.01878 of all possible original scenarios
1. PHO, 2. DAL, 3. MEM
(250/1000)*(156/750)*(199/594) = 0.01742
1. MEM, 2. PHO, 3. DAL
(199/1000)*(250/801)*(156/551) = 0.01758
1. DAL, 2. PHO, 3. MEM
(156/1000)*(250/844)*(199/594) = 0.01548
1. MEM, 2. DAL, 3. PHO
(199/1000)*(156/801)*(250/645) = 0.01502
1. DAL, 2. MEM, 3. PHO
(156/1000)*(199/844)*(250/645) = 0.01426
If you add up the decimals on the right, you get 0.09854, which means that it's only about a 1 in 10 chance that no one from outside the top three moves up. But if that
is the case, then the Suns' chances for each pick are
#1: (0.01878 + 0.01742)/(0.09854) = .367
#2: (0.01758 + 0.01548)/(0.09854) = .335
#3: (0.01502 + 0.01426)/(0.09854) = .297
(adds up to .999 due to rounding error)
So if we're all clear by the time they reveal #4, it's almost a 37% chance that the Suns are the winner.
EDIT: I forgot that Dallas has only 138 chances, not 156, because they finished tied with Atlanta. So all of those numbers are wrong, but the principle is still correct. Update coming.