Ozone is not "present in the uppermost layer of the atmosphere": its concentration peaks in the stratosphere, which is indeed higher up than the troposphere, but there are other atmospheric layers at even higher altitudes. For an introduction to the structure of the atmosphere, see https://en.wikipedia.org/wiki/Atmosphere_of_Earth#Principal_layers, and for an initial perspective on the vertical distribution of ozone in the atmosphere, see http://paoc.mit.edu/labweb/notes/chap3.pdf.
Inert chemical compounds do indeed exhibit vertical profiles that smoothly decrease with height, like CO2, for instance. However, ozone is a chemically active substance: it is continuously 'created' and 'destroyed' in the stratosphere, due to a set of chemical reactions between the molecules present in that layer and stimulated by ultraviolet solar radiation. The observed vertical profile is the net result of these chemical reactions, combined with the specifics of the stratospheric circulation of the atmosphere, which is rather decoupled from that of the troposphere.
There is a large literature on the dynamics and chemistry of the atmosphere: you will find many relevant sources by searching for these keywords on the Internet.
Ozone layer is short lived one. Ozone atoms are created and destroyed at the same time. Height is not that very high. It is almose inside the diffusive equilibrium of the atmosphere. Reactions are simple.
O2+ UV1= 2 O atoms, (1)
O+O2= O3. When this forms extra energy is given to atmosphere as heat
O3+ UV2 = O2+O (2)
Reaction (1) and (20 go on repeating and thus converting UV2 into heat. Ckorine molecules remove O. Therefore, UV2 will reach to ground therefore. This UV2 is harmful to skin.
Ozone layer is around 30 to 40 km height, if I am correct. Above that you find mostly Hydrogen. You can classify these layers by the following properties. Up to the height of 10 km, the atmosphere is thoroughly mixed. Above that constituents of gas start separating out. As you go beyond 50 km, you will find more Hydrogen as it is lightest.