Huh? A typical 10x passive probe has much less than 12pF. More in the area of 2pF, if I'm not mistaken. You shouldn't really have a problem with that.
The trimming capacitor in the probe is not to ground but in parallel to the 9M resistor.
Definitely not 2 pF.
Typical 10x 10 MOhm input passive probes have input capacitance of 8 to 15 pF, depending on brand, quality, bandwidth, etc. Higher bandwidth higher priced ones generally have lower capacitance by necessity. E.g. Tek P6139A 500 MHz has 8 pF, the P6138 400 MHz probe has 10 pF. Some high impedance probes go down to around 4 to 5 pF, but often need to compromise by having 20x attenuation in order to get there. E.g. Tek 6563A, 500 MHz, 20x, 9.5 MOhm, 4.7 pF input capacitance. Tek's best currently-made passive probes have around 4 pF input capacitance and 10x attenuation and are certainly an exception to the rule. They will set you back around $500 each.
Typical low-Z passive probes have an input capacitance of ~1 pF (0.5 to 2 pF) again depending on BW/price. Their input impedance (resistive) is typically only 500 to 1000 Ohms, which is the necessary trade-off to get the low capacitance and high bandwidth. E.g. Tek P6158 at 1.5 pF.
To go much below 1 pF, you need to go to an active FET probe, and probably an expensive one at that.