Ok, so I also did a little investigation and counted the scores for LPs only. I took the best scores each lady received this year in any competition and added them up.
The technical score for Carolina is:
3Lz – 7.6 (Worlds free)
2A – 4.3 (worlds free)
3F-3T – 10.3 (worlds free)
FCCoSp4 – 4.5 (Europeans free)
FCSp4 – 4.06 (Both worlds and Europeans free)
3L x – 6.71 (Europeans free)
3T-2T x – 7.04 (both worlds and Europeans free)
3S-2T-2L x – 9.03 (worlds free)
CCoSp4 – 4.43 (worlds free)
StSq4 – 5.9 (Europeans free)
ChSq1 – 3.4 (Europeans free)
3S x – 5.62 (2012 ! worlds free)
Note: the only jump I took from the previous season is a 3S as I believe she can actually land that jump and she will probably change her program layout so that it will come a bit earlier. The technical score is 72.69.
As for Mao we have
3A – 10.07 (4cc sp)
3F-3L< - 8.50 (4cc FS)
3Lz – 5.50 (2012 GPF FS)
3L – 6.50 (4cc FS)
FCCoSp4 – 4.50 (Worlds FS)
2A-3T x – 9.54 (worlds FS)
3S x – 5.52 (Worlds FS)
CCoSp4 – 4.43 (NHK FS)
3F-2L-2L x – 9.99 (4cc FS)
FCoSp4 – 3.77 (GPF FS)
StSq4 – 5.90 (4cc SP)
ChSq – 3.70 (GPF FS)
The technical score is 77.92. Note: I included the 3F-3L with an underrotation on a 3L. If we consider them skating clean, Mao could score about 3 points higher for this combination.
For Yuna it's quite obvious - her technical best is around 74.73.
Important thing to notice is that Yuna definitely got a clean-free-skate boost, so I would expect both Mao and Caro's score to rise up a bit if they're clean.
PCS is a different story. Prettykeys suggested calculating same exact score for all three ladies, the score being 73.61. It's a highly reasonable suggestion, as I also think if clean, the PCS will not vary much - all three are breathtaking. Though I think Caro will come a tiny bit ahead and Mao a little worse than Yuna in PCS.
Final standing in the free skate:
1. Mao 150,53 (77.92+72.61) Could be 3 points more with a rotated 3F-3L.
2. Yuna 148.34 (74.73+73.61)
3. Caro 147.3 (72.69+74.61)
I didn't do the SP scores yet, but it would highly depend on Mao's layout. If she goes for a program with 4 triples clean she will probably come far ahead of both Yuna and Caro but if she doesn't she would be definitely under Yuna, probably even Caro.
Summing up, in an ideal scenario when all 3 go clean, I imagine it's 1. Mao 2. Yuna 3. Caro. Now the only thing left is to calculate the probability of each going clean

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