I'm not a stats specialist, but I will give it a shot.
First, we can approximate the probability of each event by its empirical probability, i.e. the number of occurrences divided by the total number of trials:
$p(motif_i, condition_j) = \frac{\text{number of occurrences of motif i with condition j}}{ \sum_{i,j} \text{number of occurrences of motif i with condition j}}$
I'll use the shorthands m_1, m_2, c_1, c_2 for motifs and conditions in your table. The approximation gives the following joint distribution $p(m_i,c_j)$:
c_1 c_2
m_1 0.1 0.05
m_2 0.4 0.45
Marginal probabilities can be computed by just summing rows and columns.
Have a look at the example there: https://en.wikipedia.org/wiki/Marginal_distribution
I.e. here, $p(m_1)=0.15$ and $p(c_1)=0.5$.
Then, the mutual information can be computed from its definition:
$I(motif;condition) = \sum_{i \in [1,2], j \in [1,2]} p(m_i,c_j)\log(\frac{p(m_i,c_j)}{p(m_i)p(c_j)})$