In physics there is quanta and energy occurs per this unit. Is it it then reasonable that probability also is quantized since energy is?
Probability is a statistical measure used widely in predicting both classical and quantum mechanical behavior. It is not a variable entering the differential equations either classically or quantum mechanically.
In quantum mechanics variables turn into operators which then enter differential equations and show, depending on the boundary conditions on the solutions, a quantized behavior of the variable that the operator describes, for example "energy". Now the square of the wavefunction, which describes the state of the system as a function of energy, gives the probability of finding the system with that energy. If the boundary conditions are such that the energy values are quantized it means that the probability will be high (near 1) for the quantized states for specific energy and low to zero at the rest.
Probability always goes from 0 to 1. If one is scanning probability versus energy against an energy quantized spectrum, it will be a saw tooth plot with maxima close to 1 and minima close to 0. Measurements confirm this.
So no, probability is not a variable and cannot be quantized.