Whats is the relation between long MOSFET Turn-Off time and oscilloscope probe capacitance
The most likely cause is the parasitic capacity of transistor's gate.
Probe capacity may have some effect, but I doubt it is significant.
When you change gate voltage to high, the parasitic capacity of transistor's gate is charged directly from the input (which seems to deliver sufficient current) so the voltage changes fast.
On the other hand, when you switch input low, parasitic capacity is discharged through a resistor.
Voltage changes according to equation:
$$V=V_{high}\cdot e^{-\frac{t}{RC}}$$
\$R\$ is the resistor and \$C\$ the parasitic capacity at the gate.
\$RC\$ is called the time constant \$\tau\$ and it has a dimension of time (unit of seconds if \$R\$ is in \$\Omega\$ and \$C\$ in F).
At \$t=\tau\$, the voltage at gate equals \$V=V_{high}\cdot e^{-1}=37 \% \cdot V_{high}\$
Sufficient time for discharging is some multiple of \$\tau\$, eg at \$5\tau\$ it gets to \$0.7 \%\$.
To make the falling edge steeper, you need to decrease \$\tau\$, which is best achievable by decreasing \$R\$.
For power MOSFETs that should switch rapidly, you can use MOSFET-driver circuits, which are used to deliver high current for fast switching. (required current may be too high even for directly connecting to GPIO pin, let alone pull-down resistor).