It appears to be a 6.2nF, 5% tolerance ceramic capacitor rated for 1000V.
The Wikipedia page for capacitors includes a section on markings.
The first two digits are the value. The third is the multiplier.
For 622j it looks like this:
62pF * 10^2= 6200pF= 6.2nF.
The tolerance code "j" stands for 5%.
The voltage rating is the other number on the capacitor.
That 1000 means "1000 volts."
Here's what you need to look for in your relacement part: 6.2nF, 5% tolerance, 1000V.
I am surprised that it has gone bad. You can usually recognize a bad ceramic capacitor because they crumble or crack.
If you are using an ohmmeter to test it, that probably won't tell you much.
You need to use a capacitance meter to test it.
If you don't have one, but you do have a small AC transformer and an AC voltmeter then you could try this:
Depending on the AC powerline frequency, get a resistor of either 510k (for 50Hz) or 430k (for 60Hz.) Those are the approximate impedances for a 6.2nF capacitor at the given frequency.
Solder the resistor in series with the capacitor, and connect to the low voltage side of the transformer to the ends of the capacitor/resistor.
Measure the AC voltage across the capacitor.
Measure the AC voltage across the resistor.
Both voltages should be approximately equal.
If your capacitor is shorted (as you think) then you will measure zero volts across the capacitor and the full voltage from the transformer across the resistor.
I think you will find that your capacitor is OK.