Golly, that is so crazy high. HeaterMeter will display "No Probe" for readings which are really close to reference voltage (1-2 ADC 'ticks'). The voltage divider you've got going there is:
1.1M / (1.1M + 10k) = 0.991 = 3.2703V
While that should give a reading (1014 out of 1023) that's still pretty close to the top end. Looking at the curve for that probe, they seem particularly unsuited for reading temperatures below 100F. You'd be able to get much more accurate readings by choosing different biasing resistors for the probes.
That said, you should still be getting readings out of HeaterMeter. Without the system powered on, try checking the resistance between the metal braid on the probe wire the ground on the probe pin header (with the probe plugged in). It should read 1 ohm or less. Also try taking the same reading with the probe touching the HDMI shield which you say gives you a reading. They should be the same value.
EDIT: Oh hey you've already tested that. They shouldn't read open, that's for sure. Check to make sure the probe pin is seating properly in the jack. You should get near-0 ohm resistance between pin 1 of the probe jack header and the braid of the probe cable.