Why do planets in red dwarf star systems tend to have a higher probability to get tidally locked?
A rough back-of-the-envelope way of seeing what's going on...

The tidal force is due to the difference in gravitational force, so follows an inverse cube law:

$$F_\mathrm{tide} \propto M_\ast R^{-3}$$

where $M_\ast$ is the stellar mass and $R$ is the distance. So at the same distance from a less massive star, the tidal force will indeed be weaker. But what's usually of interest is the effect on planets in the habitable zone. As a first approximation, define the habitable zone as the location where a planet receives the same amount of insolation from its star as the Earth does from the Sun. The inverse square law then gives:

$$R_\mathrm{HZ} \propto L_\ast^{1/2}$$

where $L_\ast$ is the luminosity of the star. For main sequence stars, we can approximate using a power-law mass–luminosity relationship:

$$L_\ast \propto M_\ast^{k}$$

where the exponent $k$ is traditionally given as 3.5, although it may vary between about 2 and 4 in the mass range of interest. Combining these gives:

$$F_\mathrm{tide,\ HZ} \propto M_\ast^{1-3k/2}$$

The exponent is negative for $k &gt; \frac{2}{3}$, which is the case for the main-sequence mass–luminosity relationship. Therefore the tidal force in the habitable zone increases with decreasing stellar mass: the smaller distance to the habitable zone for these stars provides a stronger effect than the decreased mass.