How to get the duration/bitrate of a H264 file with avconv/ffmpeg

Executing avprobe test.h264 outputs

Input #0, h264, from 'test.h264':
  Duration: N/A, bitrate: N/A
    Stream #0.0: Video: h264 (High), yuv420p, 720x480, 25 fps, 25 tbn, 50 tbc

Executing file test.h264 outputs

test.h264: JVT NAL sequence, H.264 video @ L 30

Note that the file isn't damaged or corrupted, I can play it with no problem on VLC.

Is there a way to get the duration and bitrate from a raw H264 file? I read somewhere that it might be possible if I decode the file first, but I'm not sure how this can be done.

Edit #1

I'm the one creating the H264 file with a Python library called picamera.

Edit #2

Console output when running avconv -i test.h264 -f null -

avconv version 11.7-6:11.7-1~deb8u1+rpi1, Copyright (c) 2000-2016 the Libav developers
  built on Jun 17 2016 02:13:49 with gcc 4.9.2 (Raspbian 4.9.2-10)
[h264 @ 0x1bcc200] Estimating duration from bitrate, this may be inaccurate
Input #0, h264, from 'test.h264':
  Duration: N/A, bitrate: N/A
    Stream #0.0: Video: h264 (High), yuv420p, 720x480, 25 fps, 25 tbn
 Output #0, null, to 'pipe:':
  Metadata:
    encoder         : Lavf56.1.0
    Stream #0.0: Video: rawvideo, yuv420p, 720x480, q=2-31, 200 kb/s, 25 tbn, 25 tbc
    Metadata:
      encoder         : Lavc56.1.0 rawvideo
Stream mapping:
  Stream #0:0 -> #0:0 (h264 (native) -> rawvideo (native))
Press ctrl-c to stop encoding
frame=  208 fps= 68 q=0.0 Lsize=       0kB time=10000000000.00 bitrate=   0.0kbits/s
video:13kB audio:0kB other streams:0kB global headers:0kB muxing overhead: unknown

Solution

You could mux it to a container and then check

ffmpeg -i test.h264 -c copy test.mp4

ffprobe test.mp4

You can also count frames in the H264 and divide by frame rate

ffprobe test.h264 -count_frames -show_entries stream=nb_read_frames,avg_frame_rate,r_frame_rate

Duration = nb_read_frames / avg_frame_rate