  In this paper we examine properties of the variable source Sgr A* in the
near-infrared (NIR) using a very extensive Ks-band data set from NACO/VLT
observations taken 2004 to 2009. We investigate the variability of Sgr A* with
two different photometric methods and analyze its flux distribution. We find
Sgr A* is continuously emitting and continuously variable in the near-infrared,
with some variability occurring on timescales as long as weeks. The flux
distribution can be described by a lognormal distribution at low intrinsic
fluxes (<~5 mJy, dereddened with A_{Ks}=2.5). The lognormal distribution has a
median flux of approximately 1.1 mJy, but above 5 mJy the flux distribution is
significantly flatter (high flux events are more common) than expected for the
extrapolation of the lognormal distribution to high fluxes. We make a general
identification of the low level emission above 5 mJy as flaring emission and of
the low level emission as the quiescent state. We also report here the
brightest Ks-band flare ever observed (from August 5th, 2008) which reached an
intrinsic Ks-band flux of 27.5 mJy (m_{Ks}=13.5). This flare was a factor 27
increase over the median flux of Sgr A*, close to double the brightness of the
star S2, and 40% brighter than the next brightest flare ever observed from
Sgr~A*.
