Why does the Duke so readily dismisses Brabantio's suit against Othello in Othello?

This is a very important scene in Act I scene 3, but let
us remember the context, which will help us to understand the answer to the question.
The scene begins with the Duke discussing the military manoeuvres of the Turks and how
they are threatening Venice. Even before Othello and Brabantio enter and they know about
Brabantio's suit, they have already decided that this is a matter of some urgency and
that they must use Othello to counter it. Note the way the Duke, focused on the task at
hand, immediately greets Othello as he enters:

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Valiant Othello, we must straight employ
you

Against the general enemy
Ottoman.

It is clear
therefore that the Duke is keen to dismiss any issues that might prevent Othello from
starting to do his job. However, what really shows that Branatio's charge against
Othello is false is when his own daughter, who is now Othello's wife, comes to speak and
testify on Othello's behalf. Desdemona's words are enough to convince even Brabantio
that Othello did not use foul means to steal away his daughter. Note how he responds to
Desdemona's speech:

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God be with you, I have
done.

Please it your grace, on to the state
affairs;

I had rather to adopt a child than get
it.

So, as much as the Duke
is keen to focus on the affairs at hand and wants to sort out this matter as quickly as
possible, at the same time, Brabantio is so convinced by his daughter's words that he
himself relinquishes his suit against Othello and tells the Duke that he may return to
state affairs.