SNG Wiz calculates more situations than SNG-PT. SNG-PT can only calculate your shove's EV with the probabilities of the rest of the tables calling ranges. It cannot calculate what would happen if two players definitely will call.

You're going with what? Sorry I didn't get the sentence above.

Anyhow Here's the 3rd place finish probabilities from HoH 3, if that helps:

0.244
0.244
0.279
0.232

It's basic ICM analysis, nothing special, just the stacks are factored in, equal skill etc. Harrington however is a bit vague when describing how to calculate those 3rd place numbers. The first and second places are described in detail and they match the software calculators.

Note this is not (!!) a print error, Harringtons numbers add up to 1 as you can see!