It does not have much to do with entropy, rather with the way and place of ozone creation.

Stratospheric ozone is produced typically at altitude 20-30 km by UVC radiation with $\lambda \lt \pu{280 nm}$:

$$\ce{O2 + \nu -> 2 O}$$ $$\ce{O + O2 -> O3}$$

Ozone in lower troposphere troposphere is created by UVB (280-320 nm) (+UVA >320 nm ??) mostly due catalytic effects of nitrogen oxides that come typically of the oxidative smog of the Los Angeles type:

$$\ce{NO2 + \nu -> NO2^{*}}$$ $$\ce{NO2^{*} + O2 -> NO + O3}$$ $$\ce{2 NO + O2 -> 2 NO2}$$

It does not have much to do with entropy, rather with the way and place of ozone creation.

Stratospheric ozone is produced typically at altitude 20-30 km by UVC radiation with $\lambda \lt \pu{280 nm}$:

$$\ce{O2 + \nu -> 2 O}$$ $$\ce{O + O2 -> O3}$$

See ozone cycle as courtesy of @M. Farooq.

Ozone in lower troposphere troposphere is created by UVB (280-320 nm) (+UVA >320 nm ??) mostly due catalytic effects of nitrogen oxides that come typically of the oxidative smog of the Los Angeles type:

$$\ce{NO2 + \nu -> NO2^{*}}$$ $$\ce{NO2^{*} + O2 -> NO + O3}$$ $$\ce{2 NO + O2 -> 2 NO2}$$