What’s wrong with this picture?

Alice: “I just flipped a coin [large num­ber] times. Here’s the se­quence I got:

(Alice pre­sents her se­quence.)

Bob: No, you didn’t. The prob­a­bil­ity of hav­ing got­ten that par­tic­u­lar se­quence is 1/​2^[large num­ber]. Which is ba­si­cally im­pos­si­ble. I don’t be­lieve you.

Alice: But I had to get some se­quence or other. You’d make the same claim re­gard­less of what se­quence I showed you.

Bob: True. But am I re­ally sup­posed to be­lieve you that a 1/​2^[large num­ber] event hap­pened, just be­cause you tell me it did, or be­cause you showed me a video of it hap­pen­ing, or even if I watched it hap­pen with my own eyes? My ob­ser­va­tions are always fal­lible, and if you make an event im­prob­a­ble enough, why shouldn’t I be skep­ti­cal even if I think I ob­served it?

Alice: Some­one usu­ally wins the lot­tery. Should the per­son who finds out that their ticket had the win­ning num­bers be­lieve the op­po­site, be­cause win­ning is so im­prob­a­ble?

Bob: What’s the differ­ence be­tween find­ing out you’ve won the lot­tery and find­ing out that your neigh­bor is a 500 year old vam­pire, or that your house is haunted by real ghosts? All of these events are ex­tremely im­prob­a­ble given what we know of the world.

Alice: There’s im­prob­a­ble, and then there’s im­pos­si­ble. 500 year old vam­pires and ghosts don’t ex­ist.

Bob: As far as you know. And I bet more peo­ple claim to have seen ghosts than have won more than 100 mil­lion dol­lars in the lot­tery.

Alice: I still think there’s some­thing wrong with your rea­son­ing here.