Hi.
A plain 3-speed vulgar ceiling fan has a 3-in-1 inflated capacitor I want to replace : 4.5μF, 6μF and 6μF.
Why two of the capacitances are the same if the motor has 3 different speeds ?

 

Most likely the because two are capable of maintaining the two speeds sufficiently whereas at the frequency the 4.5 is used, maintains the similar phase shift.
Highly likely the capacitor is Chinese origin, BTW !

 

A start-run capacitor block where the switch combines capacitors as needed, for example:

 

Thanks, boostbuck.
Then, the switch is not a common single-contact, energizes one, two or three paralleled capacitors in series with the 'run' winding. Got it.
The 3 capacitive reactances in series allows 3 levels of current; being the faster speed the three capacitors in parallel.