An issue with Bouger-Lambert Law I'm certain that I misunderstand this law. It states that:

$$I = I_o e^{-kb} $$

and after rearranging:

$$ A = ln{I_o}-lnI $$ 

where $A$ stands for absorbance. 

1) Does is mean that when the intensity of the exiting light is very low than the absorbance is extremely high?

2) But from the graphs in my textbook, I've seen absorbance which was up to 1 or 1,2. Does it mean that most objects give little "resistance" to light? 

3) My textbook says that molar absorption coefficient depicts the probability that photon will excite the energy states (not their words exactly :) ). Than why is f(c) = epsilon a constant function? Shouldn't more concentration increase the probability of change in energy states in some for example molecule?
1) Yes that is correct.  Generally, when the intensity of the light transmitted or reflected is low, then the absorbance is high.

2) It is hard to say just what "most" means, but if we are speaking of visible light (remember absorbance is wavelength dependent), there are a LOT of colorless materials that do not absorb in the visible region.

3) Yes, more molecules will increase the probability of light being absorbed by the solution, but as you noted, the absorption coefficient is a "molar" absorption coefficient.  Therefor when using the molar absorption coefficient, the absorbance is adjusted for the number of molecules in the solution.