The Markov property is that you can model the system as being dependent on the immediately previous state + noise.
The lottery ignores the previous state and is defined purely by the noise, so it is a (trivial) markov process.
More complex systems depend on the entire history (e.g. to model a poker player you have to consider all of their actions up to the current). Newtonian systems are markov, if you know the state of the system you can run it forward in time deterministically. Even if your knowledge of the state of the Newtonian system is not fully known, you can still run the distribution of states forward in time precisely.
current_state = previous_state + process_noise
typically expressed in matrix math but the idea is as simple as that.
The lottery ignores the previous state and is defined purely by the noise, so it is a (trivial) markov process.
More complex systems depend on the entire history (e.g. to model a poker player you have to consider all of their actions up to the current). Newtonian systems are markov, if you know the state of the system you can run it forward in time deterministically. Even if your knowledge of the state of the Newtonian system is not fully known, you can still run the distribution of states forward in time precisely.
current_state = previous_state + process_noise
typically expressed in matrix math but the idea is as simple as that.