I'm trying to do text detection thanks to Naive Bayes Algorithm.

If I teach my tool: "Football is a great hobby" and assign it to the label "football", I'm totally fine with it detecting "I play football" as "football"

The issue is, if I have a sentence that does not match ANY label, the probability will be the same for all labels.

So I could obviously say that, if all probabilities are equal, I mark the sentence as not found, but if one day, two labels really have the same probability?

What do we do when we have a "not found" label with Naive Bayes algorithm?

$$\DeclareMathOperator*{\argmax}{\mathrm{arg\ max}} \hat{C_k} = \argmax_{k \in \{1, \dots, K\}} \ p(C_k) \displaystyle\prod_{i=1}^n p(x_i \mid C_k)$$
i.e. classify some observation as belonging to class $\hat{C_k}$ by taking the class that maximizes the posterior probability. This rule can be relaxed, you can, for example, say that two different classifications are equivalent, and neither is favored, if absolute difference between their predicted probabilities is not more then some $\varepsilon$.