Most probable point for finding an electron in the 1s orbital of a Hydrogen atom
It makes a difference if you look in a point or in a volume element. 

For the radial distribution we sum up the probabilities within (very thin) shells at different distances from the core.
If the radius get's bigger the volume in this shell gets bigger.
Remember that the surface of a sphere goes by $4 \cdot \pi \cdot r^2$ so the volume of the shell is essentially for all practical purposes $4 \cdot \pi \cdot r^2 \cdot \Delta r$.
At the core the radius is zero which means the volume is zero and thus the probability is zero too.

At the same time the probability of finding the electron in a point at a certain distance goes down, but the volume goes up.
Because of the scaling of the volume and the "decay" of the probability to find it in a point further away it turns out that there's a maximum of finding the electron at a certain distance away from the core (but not a single point at that distance).