Incident [TEXT]

This could be a trap. They may want to catch you in a lie, so make sure you don't say anything that isn't blatantly untrue or disprovable.

The police know you're an investigator. So it isn't that unreasonable to tell them that you were out of your house doing some work for a client. Nothing illegal. Be vague, but truthful. Don't tell them where you were specifically or who your client is. Confidentiality is important in your line of work and the police will probably understand that (although they may find it frustrating).

If they ask if there is anyone who could give you an alibi, tell them yes, but that it would compromise the aforementioned confidentiality if you did it now. This way, if they're looking to frame you, they'd have to figure out if you're lying or not about your potential alibi, and who your client is. If they press you on the clients identity, you could say "they're a semi-prominent public figure", which is true, and allows for implications as to why the secrecy is important.

Let them know that you were actually hoping to get to work on that case sometime today if possible.

Hopefully this answer will get you out of questioning, though it will also likely garner you a police tail. Keep an eye out for plainclothes officers or other cars following you during the day. (Though your assigned tail may end up being a myriad member if they're actively searching you out) So yeah, time to get a little paranoid.