Can someone tell me the fundamental reason why K+ has low concentration outside of the cell and more inside of the cell?
Why nature has done it this way around is difficult to explain. What is certain, however, is that the membrane potential which results from the imbalance of these ions across the membrane is used for a variety of purposes, such as transport of other ions and molecules, action potential generation in neurons among many other things.
How it is accomplished is mainly through the Na+,K+-Atpase pump and secondarily through Cl- channels that exchange Na+ for Cl- to lift the amount of Cl- outside the cell.
Your question isn't all that precise but I think looking at individual ionic equilibrium potentials begins to give us some understanding.
Looking at the equilibrium potentials(EK for potassium and ENA for sodium) for these two ions and their channels you have that EK = -90mV and ENA = +60mV in a typical neuron. This means that at these voltages you will have no NET flow of that ion across the membrane. Inside a cell you will have a certain amount of negatively charged ions called anions which will not diffuse, or move across the membrane regardless of the concentration gradient. To compensate for this (because the inside and outside of the cells like to have equal charges when there are not action potentials) you need a certain amount of a positively charged ion on the inside. NOW, there is no NET flow of EK at a negative voltage, this is around the same voltage of the entire membrane resting potential (this varies). If you look at the numbers and consider the voltage at which an action potential occurs, then you cannot have sodium be the cation inside the membrane since ENA = +60 since an action potential propagates when the membrane is driven towards a positive voltage.