The term “fresh pursuit” as used in §§ 23A-3-17 to 23A-3-19, inclusive, shall include fresh pursuit as defined by the common law and also the pursuit of a person who has committed a felony or who is reasonably suspected of having committed a felony in this state. It shall also include the pursuit of a person suspected of having committed a supposed felony in this state, though no felony has actually been committed, if there is reasonable ground for so believing. Fresh pursuit as used here shall not necessarily imply instant pursuit, but pursuit without unreasonable delay.