How hard is it to guess a 8 digit PIN? Say that there are different live situations where you have to select own PIN numbers.

Can someone say if it is possible to guess a 8 digit pin within 3 tries, given any methods or resources?

Is this too hard with today's technologies or possible? What about quantum computing?

And if you know, could you tell me the entropy for this case?
If a computer is doing the selection of PIN numbers, then you would be very lucky indeed to guess a PIN in three times. The entropy - assuming that all numbers are valid - is of course $\log_2{10^8} \approx 26.57$ bits.

The chances of guessing the PIN correctly in 3 tries is $$1 - \frac{x-1}{x} \cdot \frac{x - 2}{x-1} \cdot \frac{x-3}{x-2} = 1 - \frac{x-3}{x} = \frac{x}{x} - \frac{x-3}{x} = \frac{x}{x} + \frac{-x+3}{x} = \frac{3}{x}$$ where $x$ is $10^8$, so $3\times 10^{-8}$ or just $0.00000003$. This is basic math (which I managed to get wrong quite a few times, thanks to Max O. for correcting me the last time around).

Once you have a limited number of tries, the different technologies make no difference anymore. Quantum computing will allow faster computations, but since you only get 3 tries, speedup is not of any interest.

If a user creates a PIN then PIN numbers such as 00000000 are  very likely, and your chances depend very much on the person choosing the PIN. Some banks will therefore disallow the exceptionally stupid ones, leaving just the normally stupid ones. Even smart persons have been shown to be terribly bad at generating random numbers. How bad they are is hard to know, it very much depends on the target audience, I presume.