Reading one ADC input on two microcontrollers
If in doubt, use op-amp buffers to segregate each ADC from each other (and the sensor output). You do need to be aware that some op-amps won't be suitable either because of power supply restrictions or error voltages produced (information not mentioned in your question).




  In one of the microcontroller's datasheet, it's written that if I turn
  off that uC then it's pin goes to pull down mode then this might
  affect the other uC reading


It would be unusual for this to happen - it may produce a light pull down of value 100k or greater of course.


  Like putting RC filter should work I guess.


This normally works but you do create measurement bandwidth limitations that may or may not be relevant to your application.

Another option is to use an external ADC with a serial output - both microprocessors could read the serial data output with one micro controlling the clocking out of data and the other one being slave to the clocking.