Some reactions between nitrogen oxides and ozone can be the following:
$$NO\cdot(g) + O_3(g) \rightarrow NO_2\cdot(g)+O_2(g)$$
$$NO_2\cdot(g) + O\cdot(g) \rightarrow NO\cdot(g)+O_2(g)$$
Where the $NO$ when transformed to $NO_2$ stays a radical. Why is that the case? Wouldn't the unbounded electron left be used to form a double bond between nitrogen and oxygen?