  Aims. We present the first three-dimensional internal motions for individual
stars in the Draco dwarf spheroidal galaxy. Methods. By combining first-epoch
$Hubble$ $Space$ $Telescope$ observations and second-epoch $Gaia$ Data Release
2 positions, we measured the proper motions of $149$ sources in the direction
of Draco. We determined the line-of-sight velocities for a sub-sample of $81$
red giant branch stars using medium resolution spectra acquired with the DEIMOS
spectrograph at the Keck II telescope. Altogether, this resulted in a final
sample of $45$ Draco members with high-precision and accurate 3D motions, which
we present as a table in this paper. Results. Based on this high-quality
dataset, we determined the velocity dispersions at a projected distance of
$\sim120$ pc from the centre of Draco to be $\sigma_{R} =11.0^{+2.1}_{-1.5}$
km/s, $\sigma_{T}=9.9^{+2.3}_{-3.1}$ km/s and $\sigma_{LOS}=9.0^{+1.1}_{-1.1}$
km/s in the projected radial, tangential, and line-of-sight directions. This
results in a velocity anisotropy $\beta=0.25^{+0.47}_{-1.38}$ at $r \gtrsim120$
pc. Tighter constraints may be obtained using the spherical Jeans equations and
assuming constant anisotropy and Navarro-Frenk-White (NFW) mass profiles, also
based on the assumption that the 3D velocity dispersion should be lower than
$\approx 1/3$ of the escape velocity of the system. In this case, we constrain
the maximum circular velocity $V_{max}$ of Draco to be in the range of
$10.2-17.0$ km/s. The corresponding mass range is in good agreement with
previous estimates based on line-of-sight velocities only. Conclusions. Our
Jeans modelling supports the case for a cuspy dark matter profile in this
galaxy. Firmer conclusions may be drawn by applying more sophisticated models
to this dataset and with new datasets from upcoming $Gaia$ releases.
