Note
The particle で is used here because the fire is an event and not a static object.
Breakdown of yuube, chikaku no ie de kaji ga arimashita.
のno
possessive case particle
がga
subject particle
あるaru
to exist; to have; (used for non-living entities)
でde
location particle (for events and actions)
家ie
house; home
近くchikaku
neighborhood, vicinity
昨夜yuube
last night
鍵kagi
key
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