If absorbance is 0, what is the equilibrium constant?
Are we talking about uv-vis absorption?

Supposed that you are monitoring the right wavelength and that the extinction coefficients are not ridiculously small, you are outside the limits of experimental error.

If you still do not see any absorption, this means that the species isn't there (anymore).

If it isn't there anymore, it can't particiate in the equilibrium any longer - there is no measurable equilibrium anymore.

If you still need to measure something in the case of an irreversible and fast reaction, your experimental setup needs to change: 

You might need to perform time-resolved  uv spectroscopy and use a stopped-flow setup for the controlled mixing of your reactants.

If you don't have anything but a uv-vis spectrometer, a cuvette and a microliter syringe, do it the old way using the standard addition procedure


Prepare the cuvette with a solution of one reactant with a decent concentration 
Prepare a solution of the second reactant. This might be highly concentrated it you want to avoid dilution effects. If the reaction is fast, you can only measure the absorption of the first reactant and the product anyway
Measure the initial absorption of the first reactant
Add some volume of the second solution to your cuvette
Measure the uv absorption of your first reactant. Do you see any change?   
Can you measure the absorption of the product too?


Repeat steps 4-6.