I am surprised when I see that PSG have a better chance of winning against Liverpool than Liverpool! How is this possible?
As you said that's because PSG will play at their home stadium.
Bookmakers believe that PSG has a higher chance to win the first leg, but when it comes to probablity of advancing to the quarter finals, Liverpool is more favored than PSG.
The odds for liverpool to qualify for the next round are 1.57 while the odds for them to win the first leg are 2.9