JPL HORIZONS gives the distance from the observer to the target as delta
.
In Table Settings this option is 20. Observer range & range-rate.
For asteroids and comets, it can also give distance uncertainty (39. Range & range-rate 3-sigmas) as RNG_3sigma
.
You can choose units of au or km.
For example, with Table Settings: QUANTITIES=1,20,39; range units=KM, the geocentric ephemeris for asteroid (153201) 2000 WO107 around its 2020-11-29 close approach to Earth looks like:
Date__(UT)__HR:MN R.A._____(ICRF)_____DEC delta deldot RNG_3sigma RNGRT_3sig
2020-Nov-29 03:00 08 48 22.83 +14 26 33.8 4.3065970451E+06 -1.1137937 143.5915 0.0000166
2020-Nov-29 04:00 08 43 44.11 +14 51 56.9 4.3035317776E+06 -0.5890828 144.6349 0.0000171
2020-Nov-29 05:00 08 39 04.01 +15 17 00.3 4.3023570178E+06 -0.0635364 145.6159 0.0000175
2020-Nov-29 06:00 08 34 22.78 +15 41 42.1 4.3030745286E+06 0.4621549 146.5331 0.0000180
2020-Nov-29 07:00 08 29 40.62 +16 06 00.2 4.3056835832E+06 0.9872992 147.3852 0.0000185
In other words, at 05:00 UT, the asteroid is 4,302,357 ±49 km from the center of Earth.
Though its orbit is determined well enough for a permanent number designation, even 1 km precision would be unreliable.
Its perihelion distance q is only known to ±8.7 km and perihelion time tp to ±1.7 s.
New observations may improve this.
Update: new observations of (153201) 2000 WO107 improve its q to ±6.9 km, tp to ±0.3 s, and distance at 2020-11-29 05:00 UT to 4,302,522.2 ±1.1 km.
That precision is largely due to radar data, which are not always available.