Sure! Let's do the last number, 0.71. We assume that Geralt is mulliganed between cards 3 and 4 in your deck i.e. ending up in position 4 out of 16 before the replacement card is drawn. Then, the top card is drawn, and now Geralt is #3/15.
If neither Triss nor roach are mulliganed in a position above Geralt, then Geralt will end up being the top card of your deck after the mulligan, as cards in positions 1 and 2 will be drawn into your hand to replace Triss+Roach. So we need to find the probability that neither Triss nor Roach are mulliganed above Geralt.
Roach is mulliganed second, and ends up above Geralt if he is placed above card 1, between cards 1 and 2 or between card 2 and card 3 (card 3 is geralt). So there is a 3/16 chance of Roach being placed above Geralt.
Then, suppose that Roach is not placed above Geralt. The top card is drawn, and now Geralt is in position #2/15. Triss is now mulliganed, and the probability that she ends up above Geralt is 2/16.
So we have that the probability that neither Roach nor Triss ends up above Geralt is 1 - 3/16 - 13/16 * 2/16 (1 - Prob(Triss above Geralt) - Prob(Triss not above Geralt) * Prob(Roach above Geralt) ). If we didn't include the Prob(Triss not above Geralt) term we would be double counting the situations where both are placed above Geralt
The other numbers are similar, except there is a lower probability that Geralt is eclipsed since he is mulliganed into a higher position in the deck