Why is the available power in propeller engine is almost constant for every velocity?
It is a gross simplification, assuming a constant speed prop.  If a fixed pitch prop, it is non-linear.  Even with a constant speed prop it is not exactly linear. 

Lesser factors for power available are the angle of attack/angle of incidence, which will change with airspeed, assuming level flight.  Ram air is also a minor factor on some engines.

The diagram you show is a simplification meant to show you that the power is the same, regardless of airspeed, but in reality it varies.  How much? I can't say for certain in general, but on one aircraft I collected data on, I recall it varying about 6% in the 20 knot window we were looking at.  And to be clear, that was power converted to thrust, not simply power plant power.