The depletion of ozone involves the following steps:
Step 1: ${{O}_{3}}\underset{k_1}{\overset{k_2}{\mathop{\rightleftharpoons }}}\,{{O}_{2}}+O$ (fast)
Step 2: \[{{O}_{3}}+O\underset{k}{\mathop{\to }}\,2{{O}_{2}}\](slow)
The predicted order of reaction will be:

Hint: The order of reaction can be defined as the power dependence of rate on the concentration of all reactants in the slowest step. Let’s consider, for example, the rate of a first-order reaction is dependent solely on the concentration of one species in the reaction.

Complete Step by step solution:
${{O}_{3}}\underset{k_1}{\overset{k_2}{\mathop{\rightleftharpoons }}}\,{{O}_{2}}+O$ Equation (1)
 \[{{O}_{3}}+O\underset{k}{\mathop{\to }}\,2{{O}_{2}}\] Equation (2)
\[Rate=k[{{O}_{3}}][O]\] Equation (3)
\[k_1\] and \[k_2\] are rate constants for equation (1),
\[k_1[{{O}_{3}}]=k_2[{{O}_{2}}][O]\]
\[[O]=\dfrac{k_1}{k_2}\dfrac{[{{O}_{3}}]}{[{{O}_{2}}]}\]
Putting the value of [O] in Equation (3)
\[\begin{array}{*{35}{l}}
Rate=\dfrac{k_1}{k_2}\dfrac{[{{O}_{3}}]}{[{{O}_{2}}]}k[{{O}_{3}}] \\
Rate=\dfrac{k_1k}{k_2}\dfrac{{{[{{O}_{3}}]}^{2}}}{[{{O}_{2}}]} \\
\end{array}\]
Consider \[\dfrac{k_1k}{k_2}\]as a constant hence,
\[Rate\propto {{[{{O}_{3}}]}^{2}}{{[{{O}_{2}}]}^{-1}}\]

Order of reaction = 2-1=1

Additional Information:
Zero: A zero-order indicates that the concentration of that species does not affect the rate of a reaction
Negative integer order: A negative order indicates that the concentration of that species inversely affects the rate of a reaction
Positive integer order: A positive order indicates that the concentration of that species directly affects the rate of a reaction
Non-Integer: Non-integer orders, both positive and negative, represent more intricate relationships between concentrations and rate in more complex reactions.

Note: The order of reaction refers to the power dependence of the rate on the concentration of each reactant. The order of reaction is an experimentally determined parameter and can take on a fractional value. This is distinct from the molecularity (or stoichiometry) of the reaction which is the theoretical integer value of the number of molecules involved in the reaction.