jq: select dicts containing sub-dicts containing a key "b"

example-output.json

{
  "a": {
    "b": {
      "key_1": "value_1"
    }
  },
  "e": {
    "b": {
      "key_3": "value_3"
    }
  }
}

example-valid-input.json

{
  "a": {
    "b": {
      "key_1": "value_1"
    },
    "c": {
      "key_1": "value_1"
    }
  },
  "d": {
    "a": {
      "key_2": "value_2"
    },
    "c": {
      "key_2": "value_2"
    }
  },
  "e": {
    "b": {
      "key_3": "value_3"
    },
    "c": {
      "key_3": "value_3"
    }
  }
}

jq.sh

# Given valid JSON input file from colleague ...  >:-/

cat example-valid-input.json | jq '[ to_entries[] | select(.value.b) | { key: .key, value: {"b": .value.b} } ] | from_entries'