It's deterministic, no chance involved from that moment on. Transparent forging will use that information i guess.
If it'd work that way, low stakes'd never get possibilty to generate a block if there's big stake online; and inside-attack'd become cheaper too all you've to do is run biggest amount of NXT in moment of attack.
So there's hashing to hit your own Base Target with low freq. game of chances, I suppose. And if I understand TF correct, your "set to be fast" tx'll go exactly to this node that'll have closest to 100% chance of forging in nearest future calculated by analysing all forgers at moment of sending tx. Ofc, there'll be some risk node'll ruin (or whole system will) in nearest future, or another forger win a block earlier, but average time of that kind of txs will be almost "0 + nearest future".