  We present a measurement of the ratio of the top-quark branching fractions
$R=\mathcal{B}(t\rightarrow Wb)/\mathcal{B}(t\rightarrow $ $q$ represents
quarks of flavors $b$, $s$, or $d$, in the final state, in events with two
charged leptons, missing transverse energy and at least two jets. The
measurement uses $\sqrt{s}$ = 1.96 TeV proton--antiproton collision data
corresponding to an integrated luminosity of 8.7 fb$^{-1}$ and collected with
the Collider Detector at Fermilab during Run II of the Tevatron. We measure
$R=0.87 \pm 0.07$ (stat+syst), and extract the magnitude of the
Cabibbo-Kobayashi-Maskawa matrix element, $\left|V_{tb}\right| = 0.93 \pm 0.04$
(stat+syst) assuming three generations of quarks. Under these assumptions, a
lower limit of $|V_{tb}|>0.85$ at 95% credibility level is set.
