Let $[X_1, X_2, ..., X_r]$ be a set of independent $d_1 \times d_2$ dimensional random matrices with $\mathbb{E}(X_i) = 0$ and $\|X_i\| \leq B$ (bounded operator norm).
Introduce the sum of random matrices, $Z = \sum_{i=1}^r X_i$
Define matrix variance proxy:
$$\sigma^2 = \max \left( \| \mathbb{E}(ZZ^T)\|, \|\mathbb{E}(Z^TZ) \|\right) .$$
Then Bernstein inequality for rectangular matrices states that:
$$\hspace{6cm}\Pr(\|Z\| \geq t) \leq (d_1+d_2)\exp\left(\frac{-t^2/2}{\sigma^2 + Bt/3}\right)\hspace{6cm} (1)$$
So far so good, my question is: what happens with $\Pr(\|Z\|<t)$ when the parameters in (1) make the bound for the probability bigger than 1?, because that would lead to a negative lower bound for $\Pr(\|Z\| \geq t)$. Would that be a problem?